
Class L -D I L 
Book JlX 



fopyrightN 

CGEXRIGHT DEPOSm 



i 



THE ACCOMPLISHMENT RATIO 

A Treatment of the Inherited Determinants 
of Disparity in School Product 

By 
RAYMOND FRANZEN 

A.B. (Harvard), M.A. (Columbia) 
Ph.D. (Columbia) 



Teachers College, Columbia University 
Contributions to Education, No. 125 



Published by 

fEeacberg College, Columbia Umuergttp 

New York City 
1922 



Copyright, 1Q22, by Raymond Franzen 



)Ci.A696754 

f£8 16*23 



T. D 



I 



PREFACE 

The results of the experiment reported here have become so 
much a portion of my process of reasoning that duplication of 
material presented elsewhere is unavoidable. I wish in particular 
to recognize my indebtedness to the Teachers College Record 
for permission to reprint here revised portions of an article which 
appeared in the November, 1920, number of that journal. I will 
warn here any reader to whom the intricacies of a full statistical 
account are irksome that the logic and conclusions presented in 
this study are incorporated in a more palatable and abbreviated 
form in Chapter IV of Intelligence Tests and School Reorganization 
(World Book Company) . 

The work presented here has been made possible by the co- 
operation and interest of the two principals of the Garden City 
public school during the period of my work there, Miss Gladys 
Locke and Mrs. Edna Maule. I also owe any success that this 
experiment may have had to the teachers who did the real work 
of "pushing" abilities to their limit. My indebtedness to Gladys 
Locke Franzen for help in expression and correction is surpassed 
only by what I credit to her encouragement and cooperation at its 
inception. 

During the period in which this experiment was planned and 
executed it grew into a real problem through the advice of two of 
my teachers to whom I owe all such inspiration and knowledge as 
I possess — Edward L. Thorndike and Truman L. Kelley. 

Raymond H. Franzen 

Des Moines, Iowa, 1022. 



CONTENTS 

I. An Outline of the Experiment i 

The Use of Quotients and Ratios 
The Derivation of Age Norms 

A Method of Survey of Reading, Language and 
Arithmetic 

II. Statistical Treatment op the Experiment 17 

The Quotients 
The Ratios 
Summary 

III. The Psychological Conclusions of the Experiment 43 
The Neglect of Genius 
Is Genius Specialized? 
Current Psychological Opinion 
Conclusions 



PART I* 
AN OUTLINE OF THE EXPERIMENT 

THE USE OF QUOTIENTS AND RATIOS 

Standardized measurement of educational product has won its 
way to a recognized place in the school life of this country. Many 
of our larger cities have research bureaus of tests and measure- 
ments, and advanced private schools have departments of measure- 
ment. The logic of the use of statistically derived evaluations 
versus the use of opinion, swayed as it is by the haphazard captions 
of emotion and condition, has become widely recognized. The case 
of scientific measurement in education has been argued and won. 
The objections to older forms of measurement have become the 
criteria of the value of the new. 

Still administrators, although they have been convinced theo- 
retically of its importance, find it hard to see just what measure- 
ment does for their schools. They often object that measurements 
are made, the tests are carried away by the examiner, and some 
time later they are presented with a neat series of distributions 
and are told where their school stands in relation to certain other 
schools or to schools in general. This is undoubtedly a very im- 
portant piece of information; since a determination of the extent 
to which a goal has been attained forms the basis of the com- 
mendation or condemnation of the methods, curricula, and text- 
books employed in the process. But administrators want to know 
which of the various elements of school procedure are to be praised 
and which are to be blamed. 

We cannot condemn or support a whole school system on the basis 
of composite results (unless all possible educational objectives have 
been measured, and show one common drift; or unless it is neces- 
sary that the system fall or stand as a whole) since then we should 
be throwing good and bad into a common discard. We must 
measure each thing separately. We must build our ideal system of 
education synthetically, taking the best methods from each of the 

* Part of this section is reprinted with revisions from Teachers College Record, 
Vol. XXI, No. s (November, 1920). 



2 The Accomplishment Ratio 

prevalent groups of theories. There has been too much absolutism 
in education, too little of a realism that sees the good and bad in 
all and diminishes the bad and augments the good. If we adopt 
this point of view we become really empirical in our method, 
living through each educational experiment to incorporate it into a 
growing treasury of tested theory, not deducing success or failure 
from metaphysical or doctrinaire prejudice. In this administrators 
have been more scientific than those who measure. They have 
always objected that they wanted differential diagnoses. Here 
the answer to their needs must come through experimentation 
and it is only through nation-wide study and careful comparison 
and integration of results that methods of teaching can be scientifi- 
cally established. 

Three uses of measurement commonly stressed are: (i) Diag- 
nosis of degree of attainment of goal; (2) selection of method of 
attainment of goal; (3) definitive outline of goals. We have seen 
that the first two are of little immediate value to the administrator. 
The first only gives him an accurate notion of where he stands in 
any one subject without pretending to tell him why; the second 
is a promissory note. Some day we shall be able to tell him the 
best methods for the attainment of his goal. The third has slightly 
more immediate value. Measurement splits up the goals of educa- 
tion, gives them concrete formulation, allows teachers to see an 
advance in the class in one function as separate from the rest; 
allows them, for instance, to distinguish more clearly than they 
otherwise would between oral reading and silent reading, or be- 
tween addition and division. But this, too, is rather too general 
to appeal to administrative economy. One would find it very 
difficult to sell one's services as a measurer to a school board or 
a superintendent on the basis of these three values. They answer 
that universities and scientific research give them as much as they 
want of these values. What an expert on measurement could add 
in interpretation of results would seem of small additional value 
to them. 

Still there is a very marked function that such an expert can 
perform; but he must serve a fourth and fifth use of measurement 
while he serves a particular school. When he serves the first three 
he is serving the science of education and, unfortunately, no one 
school will pay him to do that. The uses of measurement that 
directly benefit any one school are: (4) Classification by information 



An Outline of the Experiment 3 

and intelligence and (5) diagnosis of individual disability. For 
the proper prosecution of these aims individual measurements and 
age norms are essential. Only with such equipment can we make 
the prognoses of future school behavior which the administrator 
so urgently needs. 

Grade norms cannot be used to make individual diagnoses. 
Though we can see by them which children are below and which 
above the level that in their grade they should attain, we cannot 
see just what administrators most need to know; namely, whether 
the retardation and acceleration are justified or not — how many 
children are working at maximum. More than that, computations 
based on grade norms are very inaccurate in individual cases 
because the variability within any grade is so great. As it becomes 
necessary to use new norms for such purposes it is important to 
have them in terms that are directly comparable to intelligence 
mensuration. 1 

First in importance is an interpretation of the meaning of an 
Intelligence Quotient. Too often it is stated as a number and 
left as a number with the belief that somehow or other that is a 
tag which carries its own divine implication. Its importance lies 
in its diagnosis of power of adaptation, and it has a high correlation 
with the maximum possible rate of school progress. Just as a pure 
information test diagnoses the neural bonds that have been formed 
in any one field, so an intelligence test diagnoses the ability to form 
bonds, to meet a new situation and form satisfactory habits — 
power to learn. It may be thought of as a diagnosis of the neural 
chemistry of the individual. As such it is not concerned with the 
connections or quantity, but rather with the quality of the neural 
tissue. 

1 For scientific purposes we want year- month means and standard deviations, that 
we may say that Charlie Jones is 2.1 S. D. above the mean for his age level, while 
Harold Smith is .1 S. D. below that mean. It is in terms such as these that we may 
be able to compare accomplishment in one function with accomplishment in another, 
progress in one with progress in another. For many of our problems we need a com- 
mon denominator of measurement so that we may compare progress between tests and 
age-groups. The best common denominator is, I believe, S. D. in an age-group. 
Thus we may locate a child in any age-group in any test and compare that location 
with the position of any other child in any other test in his age-group. 

For practical purposes, however, it is for many reasons more convenient to use 
quotients in elementary schools. Principals would rather deal with quotients since it 
is easier to explain them in terms of attainment and capacity. It is the use of such 
quotients that this thesis discusses. 



4 The Accomplishment Ratio 

As an intelligence quotient is actual mental age divided by 
chronological age — which is the normal mental level of the child's 
age-group — so it is the rate at which the child has progressed to 
mental maturity. It is his potential rate of progress. It is a division 
of what is by what normally would be. Then, when we use I Q 
we express the various degrees of power of adaptation due to 
various degrees of fitness of neural equipment to form bonds, by 
means of a diagnosis of the rate of formation of bonds which 
everyone forms sooner or later in an environment such as ours. 
It is conceivable that we might test this same power without 
testing the presence of such bonds at all. Such a test would detect 
directly the quality of the neural equipment irrespective of quantity 
or conformation. 

A ten-year-old child whose mental age is ten has progressed 
at the rate which is normal, and his I Q is i.oo. A very exceptional 
ten-year-old child whose mental age is fifteen has progressed just 
one and one half times as fast as the former, and his I Q is 1.50. 
Another exceptional ten-year-old child whose mental age is five 
has progressed at just one-half the rate of the first, and his I Q is 
.50. What we mean, then, by an Intelligence Quotient is the 
rate at which a child grows to the mental maturity of human 
beings in the world as it is. 

For purposes of presentation of a problem one can here assume 
(an hypothesis the value of which will here be determined) that 
each child can attain this rate of progress in each of the elementary 
school subjects. The degree to which this is true is the degree 
to which the I Q is a valid index of power to deal with school subjects. 
This assumes that inherited special disabilities in the school subjects 
are uncommon, that school progress is determined by the interplay 
of intelligence and environment, and that so-called interest char- 
acteristics which aid in development are the result of an earlier 
interplay of intelligence and environment. The degree to which 
educational product of children can be made to approach this 
intelligence will allow us to judge how far these factors are in- 
herited, since differences that are removable must be learned, 
not innate. 

We can the more readily see the significance of viewing a child's 
equipment in terms of educational and mental age, when we 
conceive of a Subject Quotient. This is a quotient resulting from 
the division of the age level reached in the test in question by the 



An Outline of the Experiment 5 

chronological age of the pupil. It is a measure of the rate of progress 
of the child in the school subject under consideration. Thus a 
ten-year-old child with ten-year-old ability in Thorndike Reading 
Scale Alpha 2 would have as his reading age divided by chrono- 
logical age, 1. 00. This may be called his Subject Quotient in 
Reading or his Reading Quotient. The division of what is by what 
would be if the child were normal gives the percentage of nor- 
mality, the actual rate of progress. Since the I Q is the potential 
rate of progress and the S Q the actual rate of progress, the ratio 
of S Q to I Q gives the percentage of what that child could do, that 
he has actually done. Thus a child with an I Q of 1 .32 whose read- 
ing quotient (his R Q) is 1.10, though he is doing work which is 
above normal, is not doing work which is above normal for him. 

T . RQ . 1. 10 , . 

His — — is , whereas if he were progressing at his optimum 

IQ 132 

rate it would equal — — . This — — is the same quantity as — - - 
1.32 IQ MA 

We may call this a Subject Ratio and the a\erage of Subject Ratios 
an Accomplishment Ratio. We could, if the absolute association 
between reading age and mental age were perfect, measure the 
approximation to ideal educational performance of any one child 
in any one elementary school subject through the approximation 
of this Subject Ratio to 1.00. As we will see later, Subject Quo- 
tients approach the Intelligence Quotients when special treatment 
is given; that is, the correlation of S Q and I Q becomes nearer 1.00 
and the difference between the average I Q and the average 
S Q approaches zero. It is safe then to expect these Subject Ratios 
to be at least 1 .00 before we pronounce satisfaction with the school 
product. 

There is certainly a significant relation between IQandSQ, 
and the more perfect the educational procedure has been, the more 
it has called forth all that the child is capable of, the higher it 
will be. To determine whether the quotient in any school subject 
can be greater than the Intelligence Quotient in any significant 
amount, it will only be necessary after we have perfect age norms 
by months to get that quotient amongst enough pupils whom 
we know to be working at maximum. What is significant here is 
that the more nearly any such quotient reaches or exceeds the Intel- 
ligence Quotient the more nearly has the child been brought up to 



6 The A ccomplishment Ratio 

what he is able to do under the best conditions. The Accomplish- 
ment Ratio is the degree to which his actual progress has attained to 
his potential progress by the best possible measures of both. 

This would be a mark of the child's effort, a mark of the concen- 
tration and interest that the child has in the school work, and as 
far as no inherited traits or capacities other than intelligence affect 
school work it is a measure of the efficiency of a child's education 
thus far. If there are such other innate bases, it is also a measure 
of those inherited traits and capacities or their predisposition, such 
as concentration, effort, written expression, etc. At any rate it is a 
measure of the child's accomplishment, and so of the effort and 
concentration as they really are at present working under those 
school conditions. It is an index of achievement irrespective of 
intelligence. 

A very convenient graph representing the same facts and easily 
interpreted by the teacher may be constructed thus: 

Mental Age 



o 

in 

bo 
< 



Reading Age 

Chronological Age 

Spelling Age 



Arithmetic Age 



Here it can be easily shown that Spelling Age, Reading Age, 
Arithmetic Age, etc. , are in some definite relation to both Chronolog- 
ical Age and Mental Age. Using the Mental Age line as a goal, 
these records may be kept constantly up to date. Another use of 
the Accomplishment Ratio is as the medium in which the children 
may keep records of their own work. As it is a mark in terms of 
intelligence, dull and brilliant children may compete on a parity 
to bring their Accomplishment Ratios as high as possible. 

Mainly we have advanced formal education. We have in many 
ways promoted the abilities to read, write, spell and figure. But 
our philosophy of education has advanced far beyond that. We 
have other aims in education, and consequently other methods and 
modes, which also must be measured and judged. We wish to 
promote such qualities as stability, self-reliance, concentration, 
and ambition. It does not necessarily follow that we must measure 
these things directly, although every one vitally interested in 



An Outline of the Experiment 7 

measurement cherishes the hope that we may some day measure 
their behavioristic correlates, — "For the quality of anything exists 
in some quantity, and that quantity can be measured." 

"Some of us might be entirely willing to rest the case after asking 
whether in practical school life anyone ever saw a teacher thor- 
oughly confident of teaching ideals but neglectful of reading and 
arithmetic. The fact is that the conscientious teacher always gives 
attention to both and the successful teacher is able, without omitting 
one, to cultivate the other. The theoretical possibility of thinking 
of the two results separately has little significance in dealing with 
real teachers and real schools. Good reading is a school virtue; 
and when one has measured good reading he has measured more 
than the trivial or formal side of education." 1 

This I believe to be true, but I also believe that through measure- 
ment we can actually promote those other more ethical ideals in 
education. Through classification by information and by intelli- 
gence we gain a marked increase of attention, concentration, ambi- 
tion, and other objectives, measured in part by Accomplishment 
Ratios. More discussion due to a greater homogeneity promotes 
powers of inference and insight; being only with equals promotes 
self-confidence and honor, and in many cases prevents a regrettable 
conceit among supernormals; having work to do which is hard 
enough prevents habits of indolence and carelessness so commonly 
found among intelligent children. 2 

It is a well-known fact that much work must be done in classi- 
fication to get homogeneity or real conditions of teaching. As it is, 
most teachers are talking to the middle of their classes. When 
they do they mystify the lower quarter and bore the upper quarter; 
they talk to the upper quarter and mystify the lower three quarters; 

1 Judd, C. H., "A Look Forward," in Seventeenth Yearbook, Pt. II, of the N. S. S. E., 
1918. 

2 When the disadvantages of "pushing" children are discussed, the disadvantages 
of keeping children at their chronological age levels should be considered as well. 
Although it is true that a supernormal child placed in that grade for which he is men- 
tally equipped loses much in social contact, it is also true that he loses a great deal by 
remaining in the grade where he physiologically belongs. There he develops habits 
of conceit, indolence, and carelessness. It is in all cases much better to group intelli- 
gent children and enrich the curriculum than to "push" them; but pushing may be 
better than leaving them where they belong by age. It is a possibility worth con- 
sidering that the explanation of the "peculiarities" of genius lies in the fact that he has 
never associated with equals. When his fellows are mentally his equals they are 
physically far older and when they are physically his equals they are mentally inferior. 



8 The Accomplishment Ratio 

or they talk to the lower quarter and bore the upper three quarters. 
When a child is bored or mystified his Subject Quotients become less 
while his Intelligence Quotient remains constant. Then his Accom- 
plishment Ratios become less as long as he remains in a position 
where he is being mistreated educationally. This, then, is the 
proper measure to see whether a child is classified properly or not. 
At the Garden City public school I changed as far as I was able 
the conditions of education of each child in that subject wherein 
his Accomplishment Ratio was markedly below i.oo. The con- 
centration and effort of the child were obviously low and my 
attempt was to change conditions and to promote habits of con- 
sistent work. When the Accomplishment Ratio increased I knew 
that the child was profiting, that he was working. Our objective 
was to increase Ratios of all children, not to attain any set 
standard. 

This Accomplishment Ratio would, to my mind, be an ideal 
school mark. Besides the inaccuracy of marks to-day, which are 
accurate marks only of the teacher's opinion, biased as it is by the 
personal equation of her character with that of the pupil, there is 
another fault of prevalent school marking. It is based on average 
work. The mark is the link between education in the school and 
education in the home. It gives the parents an index of the child's 
work and allows them to encourage or discourage the child's atti- 
tudes. Such indices have no real significance when they are based 
upon average development, as the parent is generally mistaken 
about the ability of the child. 

Marks given by a teacher are satisfactory only for a normal 
child with normal age for the grade. Brilliant children are over- 
praised for work which, though over the ability for the group, is 
under their own ability. Marks given to stupid children are 
misinterpreted by parents so as greatly to prejudice the effort 
of the child. Though his work may be such as to merit encourage- 
ment his mark may be very low. Teachers' marks are, aside from 
their inaccuracy, just, only in a group that is perfectly classified; 
just, only when the children are all of the same ability and all 
possess the same initial information. So far as they are unjust 
they are subversive of our aims, as they then transmit a faulty 



An Outline of the Experiment 9 

message to the home and disrupt the continuity of school and 
home education. 1 

Such marks as are here advocated would correct this feature 
of our present system, as well as the inaccuracy of our present 
marks. It is a mark which evaluates the accomplishment of the 
child in terms of his own ability. A brilliant child would no longer 
be praised for work which in terms of his own effort is 70 per cent 
perfect, in terms of the maximum of the group 90 per cent. The 
teacher gives him a mark of 90 while we mark him 70. A stupid 
child who does work which is marked 70 in terms of the maximum 
of the class but 90 in terms of his own, a limited ability, is no longer 
discouraged. His effort is evaluated, and the praise which he 
receives from home is merited and consequently economical, since 
the resultant satisfaction cements the bonds of concentration and 
attention. Such a mark is an actual index of the effort that child 
is making and consequently forms the proper link between the 
school and the home. 

Parents would need no great instruction in the interpretation of 
these marks, since they have always acted as though the other 
marks were these, and since these also are in percentage form. 
The only kind of mark they can understand is an Accomplishment 
Ratio. I found that the parents of the children at Garden City 
were more attentive to such marks than to others, and acted upon 
them more readily. Of course the parents of the very intelligent 
children, who are used to marks above 90, are surprised at first 
when you tell them that your mark of the child is 80; but upon 
explanation, which should in all cases precede the first report to 
the parents, they immediately see the value of such grading. It 
is fortunate in this connection that the greatest amount of ex- 
planation is necessary about intelligent children, as one usually 
deals then with intelligent parents. 

THE DERIVATION OF AGE NORMS 

In this study age norms were derived empirically, both regression 
lines being taken into consideration. From the point of view of 

1 Whether only the Accomplishment Ratio as a percentage should be given the 
parents, or whether they should know both the I Q and all the S Q's, is a question on 
which I am not prepared to give an opinion. I incline to believe that the parents 
should know only the final marks and am sure that I advise telling the children these 
only. 



io The Accomplishment Ratio 

statistics it becomes imperative, in order to use the technique 
here advised, to have the average age of a score — since we are 
going to predict age from score — to translate crude scores into 
indices of maturity in each subject under consideration. We are 
in error in the use of grade norms, if we find the average score of a 
grade and then, when we obtain that score in practice, say that the 
work is of that grade. To be able to say this we must know the 
average grade of a score. This takes in an entirely different cross - 
section of data. If we get the average score of all children in grade 
6, then we can predict what a 6th grade child is likely to get, but 
we can say nothing about a child who is not in grade 6. In order to 
decide that a 4th grade child has 6th grade ability, we must know 
that he has such ability that all children who share this score 
make an average grade of 6. 1 It would be wise then to get the 
regression of score on age as well as the regression of age on score, 
since they are not identical, the correlation between score and 
age being less than unity. 

We will note in passing that the data to establish these norms, 
except those of reading, are not as complete as may be desired, 
inasmuch as it was difficult to get test scores where the age in 
months also was available. However, the general data behind the 
grade norms could be used to keep the results from any crude 
error; and the averages were obtained for every month from 8 
years to 14 years, with a corresponding refinement in intervals of 
score, which made still more improbable an error in the general 
tendency of the regression lines. Then all the distributions, when 
grouped by years, were corrected for truncation; that is, the 
tendency for the brighter children of the older group to be in high 
school (the data were from elementary schools only) and the 
duller children of the younger group to be in the lower grades 
where they could not be reached was recognized and corrected by 
finding the average, standard deviation, and number of cases which 
would have existed if these forces of truncation were not operating. 
This was done by the use of the other one half of the figures compris- 
ing Table XI of Pearson's Tables for Statisticians and Biometricians . 
Dr. Truman L. Kelley pointed the way to its derivation. 

These norms differ somewhat from those derived from the grade 

1 There will be reported elsewhere a fuller consideration of this aspect of 
the techique of derivation of norms, together with a complete presentation of the 
data used to obtain the age norms herein used . 



A n Outline of the Experiment 1 1 

norms by translation of grade into average age for the grade. This 
is because the norm for a grade is the average score for a grade. 
Hence the norm of age 10 obtained in this way is the average score 
obtained by a grade whose average age is 10. Then the data used 
to obtain this average are made up of diverse ages, all of one grade, 
instead of all of one age and diverse grades. Even then, we would 
have only an average score of an age which approximates what 
we want, but is not as reliable to use as average age for a score. 

A METHOD OF SURVEY OF READING, LANGUAGE, AND ARITHMETIC 

The following procedure was employed in the experiment. The 
experiment was carried out in the public school at Garden City. 
Two hundred children were given the tests. The instructions, shown 
below, were followed in November, 1919, and in November, 191 8; 
in June, 191 9, and in June, 1920, with the exception that no 
arithmetic test was used in November, 191 8, and June, 1919. The 
Binet tests were given by the author; all of the others were given 
either by the author or the principal who was careful not to deviate 
from the directions in any way. In June of both years the author 
gave instructions for a test in one room, and then left the teacher 
in charge and went on to the next. This could be done in June of 
each year as the teachers were then fully acquainted with the 
experiment and their cooperation was assured. 

Directions 

I . Administer and score the following tests according to standard instruc- 
tions. Give all tests to grades 3 and above. 
Woody- McCall Mixed Fundamentals in Arithmetic 
Thorndike Reading Scale Alpha 2 
Thorndike Visual Vocabulary Scale, A2 
Kelley-Trabue Completion Exercises in Language 
Stanford-Binet Tests (given by the author) 

II. Translate the scores into year-month indices of maturity by means 
of the following table. (Use Mental Age for the Binet.) Assume rec- 
tilinear development, that is, that the amount of score which equals 
the developmen t of one month is the same as the amount of score which 
equals the development of any other month. Then interpolation and 
extension are allowable. Use the table in this way: Find in the table 
the scoie made by a child (for instance in the Woody-McCall); find the 
age to which it corresponds, then call this age the Arithmetic Age of 



12 



The A ccomplishment Ratio 



the child. For instance, if the score in Woody-McCall is 20, his Arith- 
metic Age is about halfway between 10 and 11 or 10 years 6 months. 



Age 


Woody-McCall 


Alpha 2 


Visual Vocab. 


Kelly-Trabue 


8—0 


12.00 


4-5^ 


3.60 


4-30 


9—0 


i5-i6^ 


4.98 


4-32 


5.00 


10 — 


18.33M 


5-46 


5 04 


5.65 


11— 


21.50 


5-94 


5-76 


6-35 


12 — 


24.66^ 


6.42 


6.48 


705 


13—0 


27.83^ 


6.90 


7.20 


7.70 



III. Arrange these Arithmetic Ages of all the children of your school in 
order from high to low with the names opposite the scores in the 
extreme left-hand column of the paper. At the right have parallel 
columns of the grades. Check the grade of each child in these columns. 
You will then have a sheet like this: 





Arith. 
Age 


Grade 


Name 


4 


5 


6 


7 


8 




B 


A 


B 


A 


B 


A 


B 


A 


B 


A 


Gertrude Smith 


180 


















# 




Saul Sampson 


176 










# 












Ed Jones 


176 
172 


















4 




George Calut 




















i 


Ida Henry 


172 
172 




















# 


Raymond Teller ....... 























# 


Ed Hoard 


172 














# 








Etc. 





Do the same with each of the tests. It is clear that, independent of 
the unreliability of the test, if your schooi were perfectly classified all 
the 8th grade children would come first on each relation sheet and then 



An Outline of the Experiment 13 

the 7th grade children, etc. You have now a picture of the overlapping 
of your grades. Regrade in reading and arithmetic. Draw horizontal lines 
across these relation sheets at the points of delineation. Divide your 
total number of children by the number of teachers available and then 
make a class division by the number of pupils, that is, Coll the upper 
one-sixth of the total number of pupils grade 8 in tjiis subject, the next 
one-sixth, grade 7, etc. Teach all grades of arithmetic at the same time 
and all grades of reading at the same time. You can now send each 
pupil to the grade in which he belongs in each subject. | | 

IV. Call each derived age a Subject Age (S A). Divide each subject age by 
the chronological age of the child. This will yield what may be called 
a Subject Quotient (SQ), previously called an Educational Quotient 
(E Q). 1 Dividing the Reading Age by the Chronological Age, ycu arrive 
at a Reading Quotient. This R Q is the rate at which the child has 
progressed in reading. We have the same kind of quotient for intel- 
ligence (Stanford-Binet I Q). This I Q is the potential rate of progiess 
of the child. 

V. The ratio of any Subject Age tc Mental Age 2 may be called a Subject 
Ratio (S R), previously called an Accomplishment Quotient (Ace Q). 1 
This Subject Ratio gives the proportion that the child has done in that 
subject of what he actually could have done, and is a mark of the 
efficiency of the education of the child in that subject tc date. The goal 
is to biing up these Subject Ratios as high as possible. When they are 
above .90, the child may be considered as receiving satisfactory treat- 
ment, providing norms for subject ages are reasonably accurate. (This 
figure, .90, applies to a Subject Ratio obtained by using a Stanford- 
Binet Mental Age.) An Arithmetic Ratio based on one arithmetic test 
and one intelligence test only is not as good as one based on three 
arithmetic tests and three intelligence tests. If Subject Ratios go far 
over 1. 00 the chances are that the Mental Age diagnosis is too low. 
The average of the Subject Ratios of a child may be called his Accom- 
plishment Ratio. 

In the application of the above instructions, whenever opportunity offers 
for classification of both subject matter and intelligence (which means many 
teachers or a large school), use a Relation Sheet (for instance for Arithmetic) 
and then have additional columns at the extreme right for intelligence 
headed A, B, C, and D. If a child's I Q is in the upper quarter of the I Q's 
of your school, check in the column A opposite his name; if it is in the upper 

1,4 The Accomplishment Quotient," Teachers College Record, November, 1920. 

2 Or the ratio of the Subject Quotient to the Intelligence Quotient, which is the 
same as the ratio of the Subject Age to the Mental Age. 



14 The Accomplishment Ratio 

half but not in the upper quarter check in B, and so on with C and D, 
Then you will be able to split each group; for instance, the one which is 
defined as 8th grade in arithmetic ability, into four sections, each of which 
progresses at a rate differing from the others. The A section will progress 
most rapidly, B next, C more slowly, and D most slowly. 

As Garden City was a small school, adjustment of procedure to 
individual differences in intelligence, besides the grouping for 
subject matter, was done mostly by pushing children. Children 
were advanced whole years (the grade they "belonged to" was the 
one in which geography and history were taught; this was their 
home grade) besides the readjustment made by the special regrading 
in reading and arithmetic. A special treatment class was formed 
where pronounced negative deviates were given special attention. 
Regrading was also instituted for spelling. Children were promoted 
whenever it was considered advisable; teachers were switched from 
subject to subject whenever that was considered advisable by the 
principal and the author. The Thorndike Arithmetics and other 
new texts were introduced to some extent. Any change possible was 

made in order to bring y~^ as high as possible. That was the goal. 

The purpose was not to prove that any certain educational pro- 
cedure would tend to promote abilities more rapidly than others, 
but that abilities could be promoted to the level of intelligence — ■ 
that intelligence is substantially the exclusive inherited determinant 
of variety of product among school children. (It is to be under- 
stood that intelligence may be, and probably is, the summation of 
thousands of inherited factors, — neutral elements, here merged 
in the broader behavioristic concept of intelligence.) 

SCIENTIFIC QUESTIONS INVOLVED IN CLASSIFICATION 

If we were able to negate other influences upon disparity of 
product, we could conclude that these were not inherited. Hence 
it would be our burden as educators so to manipulate education as 
to prevent their operation. We will attempt to analyze the de- 
terminants of individual differences in product in these children, 
to see which influences besides intelligence are part of the inborn 
equipment which is not the province of education, but of eugenics, 
to correct. No absolute validity is held for any of the conclusions 
stated here. The subject is, at best, vague and complicated; but 



An Outline of the Experiment 15 

our conclusions can be used as the basis for a good guess in school 
procedure. We can judge general tendencies from the educational 
experiences of the two hundred children whose abilities for two years 
are here charted. 

The importance to educators of the subject in hand is excuse 
enough for its treatment. All educational procedure points a pro- 
phetic finger toward the classification of pupils and a reduction of 
the individual differences of product to the inherited bases of these 
differences. 

Classification, however, needs some more accurate psychological 
foundation than the mere awareness of individual variance. We 
must know: 

1. What tests to use. 

2. How to use them. 

3. Whether abilities in reading, spelling, and arithmetic or 
their predispositions exist as special abilities, or whether children 
differ in these simply because of their innate differences of intel- 
ligence. 

4. Whether individual differences in ambition, interest, and 
industry, in so far as they influence accomplishment, are due to 
special tendencies, or whether they are learned manifestations of a 
more general heritage. 

5. How these proclivities, specific or general, are related to 
intelligence. 

Points 1 and 2 are problems of procedure which must be evolved 
from our existent knowledge of measurements and statistics. Points 
3, 4, and 5 are problems which must be solved from the evidence 
resulting from an experiment in classification using these methods. 
Points 4 and 5 introduce the vexed question of whether there is a 
"general factor" or some general inherited cause of disparity in 
school product other than intelligence. Should reading ability 
prove to be the result of certain inherited abilities, or predisposition 
to abilities, we could not use a measure of mental ability alone as 
the guide to what a child could attain in reading. If intelligence, 
however, were the only inherited prognostic factor of school achieve- 
ment, we could mark the education which had functioned in the 
child's life by the percentage which the actual accomplishment of 
the child was of the maximum accomplishment of which he was 
capable at that stage of his mental development. So, too, if interest 
in particular subjects and ambition are not mainly the result of 



1 6 The Accomplishment Ratio 

rewards and punishments of early life, but are themselves signifi- 
cantly rooted in the nature of the child, we could not condemn or 
commend curricula and methods upon a basis of the ratio of resultant 
accomplishment to mental ability, but must include a measure of 
this potentiality. The practical queries whether or not a child 
can do reading as well as he does arithmetic, whether his ambition 
and his honesty have their origin in the same strength or weakness, 
can be answered only when these problems are fully solved. The 
immediate consequences of knowing that a child can usually be 
taught to read if he does other tasks well is of obvious import. It 
would be of great service, too, to know whether lack of application 
can be corrected so as to bring concentration to the level of the 
other traits. If a child is normal in other ways and not in his 
tendency to respond to the approval of others by satisfaction, can 
this "drive" be increased or reduced to the average, or are indi- 
vidual differences in specific original tendencies basic to development 
of character, and if they are, how much influence do these differ- 
ences exert upon school accomplishment? In order to classify chil- 
dren and comprehendingly watch and control their progress we 
must know the relation of achievement to the inherited bases upon 
which it depends. We must be able to state a child's progress in 
any one school subject in terms of the potential capacity of the 
child to progress. We must know the inherited determinants of 
disparity in school product. 



PART II 
STATISTICAL TREATMENT OF THE EXPERIMENT 

In the discussion and tables which follow: 

Q stands for Quotient, which will mean a Subject Age divided 
by a Chronological Age. R stands for Ratio, which will mean a 
Subject Age divided by a Mental Age. 

A Q means Woody-McCall Arithmetic Age divided by Chrono- 
logical Age, and A R means this A A divided by Mental Age. 

V Q means Thorndike Vocabulary Age divided by Chrono- 
logical Age, and V R means this V A divided by Mental Age. 

R Q means Alpha 2 Reading Age divided by Chronological Age , 
and R R means this R A divided by Mental Age. 

C Q means Kelley-Trabue Completion Age divided by Chrono- 
logical Age, and C R means this C A divided by Mental Age. 

S Q means any Subject Quotient, that is, any Subject Age di- 
vided by Chronological Age, and S R means any Subject Ratio, 
that is, any S A divided by Mental Age. 

E Q means the average of all Subject Quotients and Ace R, the 
Accomplishment Ratio, means the average of all Subject Ratios. 

All r's are product- moment correlation coefficients, uncorrected. 
As the reliabilities (Table 4) are almost what the other coefficients 
are in June, 1920 (Table 5), it is apparent that the corrected 
coefficients, when Grade III is excluded, would all be very near 
unity at that time. 

THE QUOTIENTS 

In Table I are presented all the quotients for all periods of 
testing, grouped by children. The table, a sample of which is 
included here, 1 shows clearlv how all S Q's approach I Q as special 
treatment continues. The grades indicated in this grouping are 
as of June, 1920. Inasmuch as many double and triple promotions 
were made in an effort to get maximum product for intelligence 
invested, no conclusion can here be formed of the grade to which 

1 This table is too bulky for complete publication but may be found on file in 
Teachers College Library, Columbia University. 



1 8 The Accomplishment Ratio 

TABLE i 1 

Intelligence Quotients for All Periods Grouped by Children 

The children are arranged by grade as they were in June, 1920, and alphabetic- 
ally within the grade. The periods of testing are lettered in their chronological 
sequence; a is November, 1918, b is June, 1919, c is November, 1919 and d is 
June, 1920. * = Zero Score 

Grade 3 



Intelligence 


Test 


Arithmetic 


Vocabulary 


Reading 


Completion 


Quotient 


Period 


Quotient 


Quotient 


Quotient 


Quotient 




a 










IOI 


b 












c 


" 64 


58 




43 




d 


106 


88 




93 




a 










128 


b 












c 


80 


102 




81 




d 




152 


124 


153 




a 










116 


b 












c 


56 


90 


* 


49 




d 


94 


95 


77 


89 




a 










87 


b 












c 


90 


40 


35 


54 




d 


72 


74 


61 


52 




a 










112 


b 












c 


90 


137 


133 


112 




d 


112 


113 


121 


131 



1 The remainder of this table is riled in Teachers College Library, Columbia Uni- 
versity. Decimals are dropped in this table. 



Statistical Treatment of the Experiment 



19 



TABLE 2 1 

Group Taking All Tests at All Periods Arranged in Order of 
Magnitude of Intelligence Quotients 



Intelligence 


Arithmetic 


Vocabulary 


Reading 


Completion 


Quotients 


Quotients 


Quotients 


Quotients 


Quotients 


146 


in 


154 


164 


150 


142 


129 


135 


137 


136 


141 


109 


118 


107 


121 


139 


124 


141 


124 


134 


138 


IOI 


112 


105 


106 


138 


121 


130 


no 


109 


130 


107 


139 


135 


136 


122 


127 


130 


124 


121 


122 


113 


121 


117 


124 


122 


112 


102 


114 


129 


121 


128 


125 


128 


128 


120 


100 


116 


102 


119 


118 


117 


123 


114 


125 


117 


131 


in 


118 


124 


117 


106 


122 


112 


in 


114 


105 


126 


no 


114 


109 


83 


113 


117 


103 


107 


103 


112 


95 


103 


107 


94 


126 


94 


123 


104 


99 


117 


96 


104 


104 


103 


no 


94 


116 


103 


108 


113 


112 


106 


IOI 


100 


114 


109 


106 


100 


90 


103 


92 


92 


100 


109 


118 


108 


113 


99 


114 


104 


106 


no 


99 


114 


119 


117 


115 


98 


102 


IOI 


108 


104 


98 


99 


106 


107 


106 


97 


95 


109 


107 


105 


97 


108 


IOI 


102 


105 



1 Decimals are dropped in this table. 



20 


The A ccomplishment Ratio 






Table 2 — Continued 






Intelligence 


Arithmetic 


Vocabulary 


Reading 


Completion 


Quotient 


Quotients 


Quotients 


Quotients 


Quotation 


97 


95 


104 


89 


no 


96 


90 


104 


91 


9i 


95 


84 


99 


93 


100 


95 


90 


107 


99 


105 


95 


85 


117 


114 


103 


94 


106 


57 


89 


108 


94 


103 


103 


106 


104 


92 


96 


86 


94 


85. 


87 


83 


88 


92 


87 


87 


95 


96 


94 


102 


84 


85 


87 


93 


87 


83 


106 


91 


87 


104 


80 


77 


91 


80 


84 


80 


84 


75 


79 


84 


80 


89 


107 


88 


86 


78 


87 


90 


93 


85 


60 


69 


56 


71 


77 



these children belonged at any time except June, 1920. The cor- 
respondence betwen I Q and the S Q's in June, 1920 is further 
shown in Table 2. In this table the 48 children who took all tests 
at all periods are ranked from high to low I Q and their S Q's are 
listed opposite. The high correspondence is readily apparent. 

The intercorrelations of the quotients of these 48 cases for 
all periods may be seen in Table 3 (page 21). The correlations with 
I Q and the intercorrelations of the S Q's have increased toward 
positive unity or rather toward the limits of a correlation with 
tools of measurement such as we have used. This limit is a function 
of the reliability of the tests employed. It is customary to use a 
formula to correct for attenuation in order to find the percentage 
which the correlation is of the geometric mean of the two relia- 
bility coefficients. This is tantamount to saying that any cor- 
relation can go no higher than the geometric mean of the reliability 
coefficients of the tests used. It is better to assume that an r 



Statistical Treatment of the Experiment 



21 



can go as high as the i \lr n . r 22 since an r can go as high as the 
square root of its reliability coefficient. Dr. Truman L. Kelley 
has shown that the correlation of a test with an infinite number of 
forms of the same test would be as the square root of its correlation 
with any one other form. 

The reliabilities and limits defining a limit as the fourth root of 
the multiplied reliability coefficients are in Table 4. 

Correction for attenuation is often ridiculously high because 
the reliability coefficient of one of the measures used is so low. If 
an element is included in the two tests which are correlated, but 
not in the other forms of each test used to get reliability, the 
"corrected coefficient" is corrected for an element which is not 
chance. Whenever the geometric mean of the reliabilities is less 
than the obtained r, the corrected r is over 1. 00 and hence absurd. 1 

Therefore we use here instead, a comparison to the maximum 
possibility in a true sense. Since a test correlates with the 
"true ability" Vfm Vr n . r 2 2 is the limit of an r, its optimum 
with those tools. Although these limits apply, strictly speaking, 
only to the total correlations, since the reliability correlations are 
with all the data; we may assume that the same facts hold with 
regard to the correlations of each of the grades, that is, the reliability 
is a function of the test not of the data selected. 

TABLE 3 

Intercorrelation of All Quotients for All Periods of the 48 Children 
Who Took All Tests 







November 


, 1918 








IQ 


VQ 


RQ 


S. D. 


M 


1Q 








19. 12 


105-15 












±1-32 


±1.86 


VQ 


.72 
±.05 


• • 






20.54 
±1.41 


102.52 
±2.00 


RQ 


.64 


.64 






I9.O9 


95 90 




±.06 


±.06 






±1.31 


±1.86 


CQ 


•63 


•7i 




■77 


19-34 


99-44 




±.06 


±.05 


± 


04 


±i-33 


±1.88 



'Truman L. Kelley: Statistics, The Macmillan Co. 



22 




The Accomplishment Ratio 










Table 


3 (Continued) 












June, 1919 










IQ 


VQ 


RQ 




S. D. 


M 


IQ 


. . 


. . 






19.12 


105-15 




• • 


• • 






±1.32 


±1.86 


VQ 


•73 


. 






20.80 


H3-54 




±.05 


• • 






±i-43 


±2.02 


RQ 


.65 


•58 






H-73 


101.31 




±.06 


±.06 






±1.01 


±1.43 


CQ 


.62 


.68 


■77 




19.76 


101.04 




±.06 


±.05 


±.04 




±1.36 


±1.92 






November, 1919 










IQ 


AQ 


VQ J 


RQ 


S. D. 


M 


IQ 


. . 


. . 






19.12 


105- 15 




• • 




• • 








±1.32 


±1.86 


AQ 


.46 

±.08 




. 








14.08 
±0.97 


102.90 

±i-37 


VQ 


.86 




23 








17.07 


109.17 




±.03 


± 


09 








±1.18 


±1.66 


RQ 


.65 




.56 




71 




13-91 


101.42 




±.06 


± 


07 


± 


05 




±0.96 


±1-35 


CQ 


•79 




•47 




.83 


.82 


17.53 


105.21 




±.04 


± 


.08 


± 


.03 ± 


•03 


±1.21 


±1.71 






June, 1920 










IQ 


AQ 


VQ 1 


IQ 


SD 


M 


IQ 


. . 


. . 






19.12 


I05.I5 




• • 




• 








±1.32 


±1.86 


AQ 


-73 
±.05 




• 








I4.IO 
±0.97 


101.79 
±i-37 


VQ 


.81 




60 








18.89 


108.94 




±.03 


±. 


06 








±1.30 


±1.84 


RQ 


•79 




68 




87 




16.43 


104.94 




±.04 


±. 


05 


± 


02 




±1.13 


±1.60 


CQ 


.84 




77 




78 


84 


15.87 


108.08 




±.03 


± 


04 


± 


04 ± 


03 


±1.09 


±1.54. 



Statistical Treatment of the Experiment 



23 







TABLE 4 










Reliability Coefficients 






One Form of 


Two Forms of 


One Form with 


Two Forms with 




Each Test 


Each Test 


an Infinite Num- 


an Infinite Num- 






(By Brown's 


ber of Forms 


ber of Forms 






Formula) 








rn 


Yn 


Vru 


Vni 


Intelligence 


.888 


. . 


.942 




Quotient 


(by Brown's Formula) 1 






Arithmetic 










Quotient 


.824 


.904 


.908 


.951 


Vocabulary 










Quotient 


.820 


.901 


.906 


•949 


Reading 










Quotient 


.866 


.928 


.931 


.963 


Completion 










Quotient 


.883 


•938 


.940 


.968 



Limits of the r's = 4 Vni x 7-22 

Nov. 1918, 
June and Nov. 1910 

•925 
.924 



•936 



June 1920 
.946 

.946 

•953 



I Q and A Q 
I Q and V Q 
I Q and R Q 

IQ and CQ .941 .955 

The limits of the June, 1920 r's are naturally somewhat larger than the others 
since two forms of tests (except the Binet) were used; the unreliability of the quantita- 
tive indices is therefore lower and hence the correlation with I Q may be larger. 

The correlations in 1920 of another group — the whole school 
except Grade III — are reproduced in Table 5. Grade III was 
excluded since here there had as yet been little chance to push the 
r's. Partials were obtained with these data (Table 6). Little 
faith may be placed in the relative sizes of these partials, much 
because the r VQRQ is here only .73 and, in the data presented 
in Table 3, it is .87. This is due to the fact that the data in 
Table 3 cover all periods (2 years) while those in Table 5 cover 

1 This correlation was obtained by correlating one half of the Binet against the other 
one half and then using Brown's Formula to determine the correlation of a whole 
Binet against another whole Binet. 



24 The A ccomplishment Ratio 

TABLE 5 

Intkrcorrelation of All Quotients in June, 1920. All Children 
Exclusive of Grade 3 are Here Represented 





The P. E. 


's are all less than 
N = 81 


•05 




Arithmetic 
Quotient 


IQ 

•733 




Arithmetic 
Quotient 


Vocabulary 
Quotient 


Reading 
Quotient 


Vocabulary 
Quotient 


.837 




.628 






Reading 
Quotient 


•758 




.694 


•734 




Completion 
Quotient 


.821 




.770 


.825 


.801 



only one. This difference has comparatively slight influence on 
our general conclusions; but it makes a huge difference in the cor- 
relation of R Q and V Q when I Q is rendered constant, whether 
the one or the other set of data is used. Moreover, the whole 
logic of arguing for general factors by reduction of partial correla- 
tions from the original r has been called gravely into question 
in Godfrey H. Thomson's recent work on this subject: "The Proof 
or Disproof of the Existence of General Ability." Thomson shows 
that partial correlation gives one possible interpretation of the 
facts, but not an inevitable one. Thus we cannot say that because 
RQ and I Q and RQ and AQ are highly correlated, correlation 
of I Q and A Q is dependent upon R Q. We can say, however, 
that it is likely to be. I Q and A Q may be correlated by reason of 
inclusion of some element not included at all in R Q. The higher 
the correlations which we deal with the less we need worry about 
this, and of course correlations of unity exclude any such con- 
sideration. 

I therefore draw no conclusions from the comparative size of 
these partials, nor do I get partials with any of the other data, 
and rest the case mainly on the high r's between I Q and S Q's in 
1920; increase in correspondence of the central tendencies and 
range of the S Q's by grade with the central tendency and range 



Statistical Treatment of the Experiment 25 

of the I Q's of the same data; small intercorrelation of S R's and 
negative correlation of Ace R with I Q. 

The general lowness of the partials (Table 6) does, however, 
indicate the great causative relation between I Q and disparity 
of product. The elements still in here are common elements in 
the tests and the mistreatment of intelligence. 

TABLE 6 
Partial Correlations of Quotients Irrespective of Intelligence 

Quotients 

N = 8i 



Vocabulary 
Quotient 

Reading 
Quotient 

Completion 
Quotient 

What happened by grade in 1918-1919 is summarized in Table 

7. What happened by grade in 1919-1920 is summarized in Table 

8. Since there were many changes in personnel from 1918-1919 
to 1919-1920, we need expect no continuity from Table 7 to Table 
8. For the continuous influence of the two years, see Table 3, 
which includes 48 children taking all tests at all periods. 

TABLE 7 

All Correlations, Means, and Standard Deviations by Grade, Showing 

Progress from November, 1918 to June, 1919 

I stands for Intelligence Quotient R stands for Reading Quotient 

V stands for Vocabulary Quotient C stands for Completion Quotient 



Arithmetic 
Quotient 


Vocabulary 
Quotient 


Reading 
Quotient 


.04 

rh.07 






•31 
±.0 7 


.28 
±.07 




•43 
±.08 


•44 
±.06 


•47 
±.06 



GRADE 




r 






M 




s. 


D. 




Nov. 


June 




Nov. 


June 




Nov. 


June 


IV 


.467 


.633 


I 


IO9.89 


II3.20 


I 


12.83 


15-49 




±.12 


±.07 




dbl.98 


±1.91 




±1.40 


=±=1.35 


III IR 


•541 


.492 


V 


96.II 


IO9.9O 


V 


21.21 


18.69 




±.II 


zfc.09 




±3-28 


±2.30 




±2.32 


±1.63 


IC 


.641 


.386 


R 


82.26 


IOI.4O 


R 


22.58 


15-85 




±.09 


±.II 




±3-49 


±i-95 




±2.47 


±i-38 








C 


86.89 
±3-52 


108.40 
±1.94 


C 


22.76 
±2.49 


15-79 

±1.37 



N 



19 30 



26 



GRADE r 

Nov. 



The A ccomplishment Ratio 
TABLE 7 (Continued) 
M 



IV .724 
±.07 



June 
.819 
±.05 



Nov. 
I 105.90 
±2.73 



June 
IO4.82 
±2.98 



S. D. 

Nov. June 

I 18.08 I8.2I 

±1-93 ±2.11 



IV I R .665 .845 V 97.20 108.53 v 17.26 24.92 

±.08 ±.05 ±2.60 ±4.08 ±1.84 ±2.88 

IC .596 .717 R 91.06 107.82 R 27.85 10.35 

±.10 ±.08 ±4.20 ±1.69 ±2.97 ±1.20 



C 101.45 108.12 C 21.53 17-75 

±3.25 ±2.90 ±2.30 ±2.05 



N = 



17 





IV 


.887 


.822 


I 


101.64 


99.42 


I 


24.76 


17.63 






±.04 


±.05 




±3.56 


±2.73 




±2.52 


±1-93 


V 


IR 


•799 


.832 


V 


100.59 


in. 58 


V 


26.71 


19.78 






±.05 


±.05 




±3.84 


±3- 06 




±2.72 


±2.16 




IC 


.818 


.890 


R 


94-59 


101.42 


R 


22.10 


12.56 






±.05 


±•03 




±3.18 


±1.94 




±2.25 


±i-37 










C 


97.00 

±3.24 


102.68 

±2.74 


C 


22.52 
±2.29 


17.71 
±1.94 


N = 




22 


19 
















IV 


•793 


.772 


I 


109.90 


115-90 


I 


23-45 


24.38 






±.08 


±.09 




±5.00 


±5.20 




±3-54 


±3-68 


VI 


I R 


•497 


.726 


V 


108.00 


126.80 


V 


30.20 


25-25 






±.16 


±.IO 




±6.44 


±5-39 




±4-55 


±3.81 




IC 


.798 


.891 


R 


103.10 


107.20 


R 


13-77 


20.62 






±.08 


±.04 




±2.94 


±4.40 




±2.08 


±3-ii 










C 


108.90 

±3-25 


117. 10 
±4.01 


C 


1523 
±2.30 


18.81 
±2.84 


N = 




10 


10 















I V . 625 . 504 I 99 . 29 98 . 92 I 1 1 . 1 1 1 1 . 45 

±.11 ±.14 ±2.00 ±2.14 ±1.42 ±1.51 

VII IR .622 .709 V 109.43 115.23 V 14.07 1743 

and VII ±.11 ±.09 ±2.54 ±2.95 ±1-79 ±2.31 



Statistical Treatment of the Experiment 27 
TABLE 7 {Continued) 

GRADE r M S. D. 

Nov. June Nov. June Nov. June 

IC .782 .730 R 97.00 98.85 R 12.59 15-77 

±.07 zb.09 ±2.27 ±3-26 ±I.6l ±2.09 



N = 14 



C 102.43 95.85 C 13.49 17.72 

±2.43 ±3-3i ±1.72 ±2.34 



IV 


.685 


.680 


I 


105.07 


106.88 


I 


19-34 


18.45 




±.04 


±.04 




±1.41 


±1.32 




±1 .00 


±0.93 


I R 


.568 


.626 


V 


101. 12 


112.67 


V 


22.83 


21.58 


Total 


±.05 


dz.04 




±1.67 


±i-54 




±1.18 


±1.09 


I C 


•639 


.702 


R 


92.40 


102.91 


R 


22.65 


15-27 




±.04 


±.04 




±1.66 


±1.09 




±1. 17 


±0.77 








C 


98.08 
±i-57 


106.27 
±1.30 


C 


21.48 
±1.11 


18.19 
±0.92 


N = 


85 


89 















TABLE 8 

All Correlations, Means, and Standard Deviations of Quotients by 
Grade, Showing Progress from November, 1919 to June, 1920 

I stands for Intelligence Quotient 
V stands for Vocabulary Quotient 
R stands for Reading Quotient 
C stands for Completion Quotient 
A stands for Arithmetic Quotient 

r M S. D. 

Nov. June Nov. June Nov. June 

I A .413 .709 I 102.00 105.53 I 9-6o 10.89 

±.16 ±.08 ±1.87 ±1.68 ±1.32 ±1.19 

III IV .649 .667 A 82.75 97.84 A 15.88 18.62 

±.11 ±.09 ±3.09 ±2.88 ±2.19 ±2.04 

I R .651 .609 V 94.00 103.47 V 33.44 27.66 

±.11 ±.10 ±6.51 ±4.28 ±4.60 ±3.03 



28 



The A ccomplishment Ratio 
TABLE 8 {Continued) 



GRADE 




r 






M 




S.D 








Nov. 


June 


Nov. 


June 




Nov. 


June 




IC 


.612 


.719 


R 87.59 


93-88 


R 


32.06 


19.02 






db.I2 


±.0 7 


±6.24 


±3.21 




±4.41 


±2.27 










C 90.17 


96.84 


C 


28.82 


25-59 










±5-58 


±3.96 




±3-95 


±2.80 


TV = 




12 


19 














I A 


.426 


•725 


I 1 1 1 . 48 


113.00 


I 


14-73 


15.04 






±.IO 


±.06 


±1.85 


±i-93 




±1.30 


±1.36 


IV 


IV 


•635 


.772 


A 94.07 


1 1 1 . 08 


A 


12.34 


15.02 






±.075 


±.05 


±i-55 


±1.99 




±1.09 


±1.40 




I R 


.316 


•569 


V 109.79 


115-61 


V 


16.97 


18.39 






±.II 


±.09 


±2.13 


±2.34 




±1.50 


±1.66 




IC 


•594 


.837 


R 99.31 


no. II 


R 


17.89 


14.67 






±.08 


zb.04 


±3.24 


±1.67 




±1-58 


±1.32 










C 108.14 


118. 14 


C 


15-51 


12.70 










±i-94 


±1.62 




±i-37 


±1.15 


N = 




29 


28 














I A 


.698 


.713 


I 103.72 


98.83 


I 


19-57 


18.84 






±.07 


± 


07 


±2.69 


±2.65 




dzi.91 


±1.87 


V 


IV 


.881 




908 


A 87.58 


99.71 


A 


12.43 


16.47 






±.03 


± 


02 


±1.71 


±.2.2-] 




±1.21 


±1.60 




I R 


•773 




89I 


V 109.00 


IO5.I7 


V 


15-58 


19.97 






±.06 


=fc 


03 


±2.14 


±2.8l 




±1.52 


±1.99 




IC 


.786 




•923 


R 104.46 


IO3.OO 


R 


16.99 


17.07 






±.05 


± 


02 


±2.34 


±2.40 




±1.65 


±1.70 










C 107.00 


IO3.48 


C 


16. 12 


1451 










±2.22 


±2.04 




±i-57 


±1.44 


N = 




24 


23 














I A 


•533 


.805 


I 102.43 


105 -39 


I 


11. 61 


13-56 






±•13 


d=.o6 


±2.09 


±2.16 




±1.48 


±1.52 


VI 


IV 


•774 


.858 


A 91-43 


I04 .53 


A 


H-43 


II. 31 






±.07 


zb 


04 


+2.06 


±1-75 




±1.46 


±1.24 



Statistical Treatment of the Experiment 
TABLE 8 (Continued) 



2 9 



GRADE 


\ T ov. 


r 

June 




Nov. 


M 
June 


S. D 

Nov. 


June 




I R 


.420 

±•15 


.661 
±.09 


V 


106.07 

±2.15 


II2.94 

±1.74 


V 11.93 

±1.52 


IO.94 
±1.23 




I C 


•739 

±.08 


.620 
±10 


R 


96.64 

±2.23 


106.20 
±i-79 


R 12.38 
±1.58 


11.88 
±1.27 


.V = 




H 


[8 


cj 


100.36 

±2.51 


107.61 

±1.68 


C 13-95 

±1.78 


10-55 

±1 . 19 




I A 


.740 
±.09 


•795 
±.07 


I 


107.27 
±4.74 


100.58 

±2.85 


I 23.29 
±3-35 


19.78 
±2.72 


VII 


IV 


.867 
±.05 


.718 
±.09 


A 


100.00 

±1.86 


99-31 
±2.06 


A 9.26 

±i-33 


11.00 

±i-45 




I R 


.862 
±.05 


•799 
±.07 


V 


114.36 

±3-89 


108.75 
±2.81 


V 19.15 

±2.75 


14.42 
±1.98 




IC 


•833 
±.06 


.677 
±.11 


R 


101.73 
±2.50 


98.58 
±2.25 


R 12.28 
±1.77 


n.56 
±i-59 


N = 




11 


12 


C 


105.82 

±3-54 


101.42 
±3.12 


C 17.41 
±2.50 


16.02 

±2.21 




I A 


.663 
±.11 


.796 
±.07 


I 


104.83 
±3-Oi 


108.79 
±3-29 


I I5-46 
±2.13 


18.25 
±2.33 


VIII 


IV 


.828 
±.06 


•750 

±.08 


A 


92.92 
±1-99 


93.86 
±1.76 


A 10.20 

±1.40 


9-74 
±1.24 




I R 


•775 
±.08 


.722 

±.08 


V 


1 1 1. 67 
±3.20 


117. 21 

±2.53 


V 16.44 
±2.26 


14.02 
±1.79 




I C 


.838 
±.06 


.868 
±.04 


R 


100.83 
±2.24 


104.38 

±3.72 


R n.52 
±i-59 


20.62 
±2.63 


N = 




12 


14 


C 


104.92 
±3-53 


109.64 

±3-14 


C 18. 11 
±2.49 


17.41 
±2.22 



30 




The A, 


ccomplishment Ratio 












TABLE 8 {Continued) 










r 








M 




S. D. 




GRADE 


Nov. 


June 




Nov. 


June 




Nov, 


June 


IA 


•576 


.686 


I 


I06.02 


IO5.87 


I 


16.73 


16.87 




±•05 


±.03 




±1.12 


±1.07 




±0.79 


±0.75 


Total 1 V 


.679 


.727 


A 


91-35 


102.01 


A 


13.22 


15.61 




db.04 


±•03 




±0.88 


±0.98 




±0.62 


±0.69 


I R 


.529 


.609 


V 


107-95 


IIO.54 


V 


19.76 


19.57 




±•05 


±.04 




±1.32 


±1.24 




±0.93 


±0,87 


IC 


.678 


•73i 


R 


99.22 


I03.65 


R 


18.85 


17.12 




±.04 


±.03 




±1.26 


±1.08 




±0.89 


±0.76 








C 


104.06 
±1.26 


108.00 
±1.14 


C 


18.87 
±0.89 


18. II 
±0.8l 


N = 


102 


114 















Note — Totals without Grade III are much higher than these (Table 5). 
Grade III has many children in it who have not been long enough in an academic 
situation to allow their S Q's to go as high as they may. 



It is proper to note here that not much can be expected from 
Grades III and VIII and from totals including Grade III, since 
children in Grade III have not been there long enough to be pushed, 
and children in Grade VIII have been pushed beyond the limits 
which the tests used will register. Our logic is one of pushed cor- 
relations. If the association of I Q and the S Q's is what we are 
attempting to establish, it is necessary to show: 

1 . That the r comes near unity; 

2. That the central tendencies come near coincidence; 

3. That the S. D.'s come near coincidence. 

The value of the r is obvious; the value of coincidence of means 

becomes clearer if we think of SffQ-EQ) , the average difference 

n 

of potential rate of progress and actual rate of progress. This 
average of differences is the same as the difference of the averages, 
which is more readily calculated. Obviously, if we wish to use 
an Ace R, it is necessary to show more than correspondence when 



Statistical Treatment of the Experiment 3 1 

differences in average and spread are equated as they are by the 
correlation coefficient. Besides, coincidence of M's, correspondence 
of S. D.'s is also necessary since a correlation might be positive 
unity, the M's might be equal, and still the spread of one measure 
might be more than the spread of the other. If the spreads are the 
same and the M's are the same, and the correlation is positive 
unity, each x must equal its corresponding y. Then b l2 = b 2 i = 1.00; 
and the M's being equal, the deviations are from the same point. 
Therefore, we will attempt to measure similarity of M's and 
S. D's as well as r. 

It will be observed that both Tables 7 and 8 give evidence of 
each of these tendencies in all grades. In Table 8 marked progress 
in arithmetic is apparent. This is due to re-classification in terms 
of the Woody-McCall test, which was not done in 1918-1919. 
In 1918-1919 no arithmetic test was given and all re-classification 
was in terms of reading, being done on the basis of both reading 
tests. Spelling re-classification was done each year, but the data 
were not treated in this manner. It can be said that wherever 
re-classification in terms of intelligence and pedagogical need was 
undertaken the desired result of pushing the S Q's up to I Q was 
hastened. Of all the remedial procedure, such as changing teachers 
and time allotment and books and method, all of which were 
employed to some extent, it is my opinion that the re-classification 
was more important than everything else combined. 

It is noticeable that when r's approach the limit which the 
unreliability of the test allows them, they drop down again. This 
is probably due to continued increase of S Q's over I Q. Of course, 
for some S Q's to be greater than I Q out of proportion to the 
general amount lowers the correlation as much as for some to lag 
behind. When the S Q's of the children of lower intelligence 
reach their I Q they continue above. This, of course, is due to 
errors in establishment of the age norms. The norms are not 
limits of pushing, though an attempt was made by correction for 
truncation to get them as nearly so as possible. It is to be noted, 
however, that these norms are up the growth curve, that is, reading 
age of 10 means a score such that the average age of those getting 
it is 10, not the average score of children whose mental age is 10. 
The average reading achievement of children all ten years old 
chronologically is higher than that of a group all mentally ten, 
since many of the mentally advanced have not been pushed in 



32 



The Accomplishment Ratio 



product. The group used here to establish norms gives more nearly 
pushed norms than the others would. 

The tendency of the low I Q's to go over unity in their S R's is 
apparent in Table I and in Table 12 and also in the negative cor- 
relation between Ace R and I Q. 

In both years some second grade children were advanced to 
Grade III during the year. This accounts for the low r's in June, 
1919, but in 1 91 9-1920 the Grade III correlations are raised and 
the means raised toward the M IQ , even though some second grade 
children were put in this group during the year. 



TABLE 9 

Summary of Progress in Arithmetic by Increase in r, Decrease in M! q — M a q 

and Decrease in Difference of Standard Deviations 

Irrespective of Direction 



GRADE 


r 




Average Intelligence 

Quotient Minus 

Average Arithmetic 

Quotient 


Difference of 

Standard Deviations 

Irrespective of 

Sign (of I Q and Arith. Q) 




Nov. 


June 


Nov. 


June 


Nov. 


June 


III 


.413 
±.16 


.709 

±.08 


19.25 

±2.87 


8.16 
±2.05 


6.27 

±2.04 


6.63 

±i-45 


IV 


.426 
±.IO 


.725 
±.06 


7.41 
±1.84 


O.46 
±1.50 


2-39 
±1.29 


0.47 
±1.02 


V 


.698 
±.07 


•713 
±.07 


16. 14 
±1-93 


0-54 

±1.84 


7.14 

±i-37 


2.06 
±1.30 


VI 


5-33 
±•13 


.805 
±.06 


11.00 
±2.01 


3.OO 
±1.19 


0.19 

±1.42 


1.63 
±0.85 


VII 


.740 
±.09 


•795 
±.07 


7.27 
±3.58 


O.62 

±2.33 


14.03 
±2.53 


8.15 
±1.63 


VIII 


.663 
±.11 


.796 
±.07 


11.92 

±2.25 


14.93* 
±2.69 


5.26 
±1-59 


*8.53 
±i-54 


Total 


.576 
±.05 


.686 
±.03 


14.67 
±0.94 


3-72 
±0.81 


3.5i 
±0.67 


1. 16 

±0.57 



* These quantities do not decrease because a perfect score on the arithmetic test was 
too easy to obtain at this time. The children had reached the limits of this test. 



Statistical Treatment of the Experiment 



33 



TABLE 10 

Summary of Progress in Reading, November, 191 8 to June, 19 19, by In- 
crease in r, Decrease in Mi q— M rq , and Decrease in Difference 
of Standard Deviations Irrespective of Sign 









Average Intelligence 


Difference of 


GRADE 


r 




Quotient Minus 

Average Reading 

Quotient 


Standard Deviations 

Irrespective of 

Sign (of I Q and R Q) 




Nov. 


June 


Nov. 


June 


Nov. . 


June 


III 


•541 
±.II 


.492 
±.09 


27.63 


II.80 


9-75 


O.36 


IV 


.665 
±.08 


•845 
±•05 


14.84 


—3.00 


9-77 


7.86 


V 


•799 
±.05 


.832 
±•05 


7-05 


— 2.00 


2.66 


5-07 


VI 


•497 
±.16 


.726 

±.10 


6.80 


8.70 


9.68 


3-76 


VII 


.622 


.709 


2.28 


O.07 


1.48 


5-98 


3 of VIII 


dz.II 


d=.09 










Total 


.568 
±.05 


.626 
±.04 


12.67 


3-97 


3-31 


3-i8 






TABLE 11 









Summary of Progress in Reading, November, 1919 to June, 1920, by In- 
crease in r, Decrease in Mt. q— M r q , and Decrease in Difference 
of Standard Deviations Irrespective of Sign 



grade 




r 


Average Intelligence 

Quotient Minus 

Average Reading 

Quotient 


Difference of 
Standard Deviations 
Irrespective of 
Sign (of I Q and R Q) 




Nov. 


June 


Nov. 


June 


Nov. 


June 


III 


.651 
±.II. 


.609 

zb.IO 


14.41 

±5-22 


11-57 

±2-55 


22.46 
±3-69 


8.62 
±I.8l 


IV 


.316 
dz.II 


•569 
±.09 


12.17 
±2.41 


2-43 

±1.78 


3-i6 
±1.70 


O.76 
dzl.26 


V 


•773 
dz.06 


.891 
±•03 


—O.74 

±1.72 


—4.17 
±1.20 


2.58 
±1.22 


1.77 

±0.85 


VI 


.420 
±•15 


.661 
±.09 


5-79 

±2-33 


O.9O 
±1-53 


0.77 
±1.65 


O.87 
±1.09 


VII 


.862 
±.05 


•799 
±.07 


5-54 
±2.88 


O.92 
±2-54 


11.00 
±2.03 


8.31 
±1.80 


VIII 


•775 
±.08 


.722 
±.09 


4.00 
±1.90 


4-43 
±2.64 


3-94 
±1.92 


2.41 

±1.87 


Total 


•529 


.609 


6.80 


2.86 


2. 12 


0.06 




±.05 


±.04 


±1.16 


±0.30 


±0.82 


±0.67 



34 The A ccomplishment Ratio 

The changes in rates of progress are expressed in summaries 
by subject matter in Tables 9, 10, and 11. Approach of Arithmetic 
Quotient to Intelligence Quotient is measured in Table 9 by: 

1. Comparison of r in June with r in November. 

2. Comparison of M IQ — M AQ in June and M IQ — M AQ in 
November. 

3. Comparison of S. D.'s of Arithmetic and Intelligence Quo- 
tients in June and November. 

The P. E.'s of each of these differences were obtained by 

P. E. = P. E. +P. E. - 2 r n P. E.i P. E. 2 

diff 1 2 

The only M IQ — M SQ in Table 9 which does not show a decrease 
at least two times as large as the P. E. of either of the elements 
involved, is the 8th grade; and this is due to the limits of the test 
used. As mentioned before, the 8th grade did not register its true 
abilities in June since a perfect, or nearly perfect, score in the test 
was too easy to obtain. The small arithmetic S. D.'s in Grade 8 
and consequent great S. D. IQ — S. D. SQ is due to the same cause. 

Tables 10 and 11 present the summary of facts with regard 
to Thorndike Reading Quotients, the first and second years respect- 
ively. 

THE RATIOS 

The discussion which follows concerns Ratios, not Quotients. 

In Table 12 are presented the Subject Ratios in the same order 

as the Quotients appear in Table I. 1 There plainly is a rapid 

SQ 
rise of y-^ from period to period, excluding all pupils who did 

not take all tests and excluding Grade III; which includes all 
children taking all tests who were in school in June, 1920, and were 
Grade IV and above in November, 191 8. The average Ace R is 
98.24 in November, 1918, and 102.78 in June, 1920. The average 
I Q for these children is 105.22. The S.D. AccR1918 is 11.17; 

1 Table 12 is too bulky for complete publication. The first page is reproduced here 
and the complete table is filed at the library. Teachers College. Columbia University. 



Statistical Treatment of the Experiment 35 

TABLE 12 

Intelligence Quotients and Subject Ratios for All Periods Grouped 
by Child. The Order of Entries is Just as in Table i 

Grade III 

Intelligence Arithmetic Vocabulary Reading Completion 

Quotient Ratio Ratio Ratio Ratio 

101 b 

c 63 57 - - 43 
d 105 87 92 



a 
128 b 



c 62 80 63 

d 119 97 120 



a 
116 b 



c 48 78 * 42 

d 81 82 66 77 



a 
87 b 



c 103 46 40 62 

d 83 85 70 60 

c 80 122 119 100 

d 100 101 108 117 



a 
101 b 



84 93 37 55 

d 90 110 98 92 



a 
90 b 



c 76 58 72 89 

d 68 121 77 102 

105 b 

c 60 43 57 

d 104 95 83 66 

The remainder of this table is filed in Teachers College Library, Columbia Uni- 
versity. 



36 



The Accomplishment Ratio 







TABLE 13 














Means 












Nov., 1918 




June, ioiQ 




] 


^OV., IOIQ 


June, 1920 


Arithmetic 
Ratio 












89.02 
±1.05 


97.16 
±1.07 


Vocabulary 
Ratio 


98.96 
±1.48 




III. 44 
±I.6l 






106.20 
±0.90 


IO7.61 
±0.93 


Reading 
Ratio 


96.47 
±1.19 




IOI.96 

±1.18 






98.98 
±1.03 


100.60 
±0.97 


Completion 
Ratio 


99.76 
±1 II 




IOI.83 
±1.23 






IOI.67 
±0.93 


103. 10 
±0.85 




Standard Deviations 








Arithmetic 
Ratio 












12.03 
±0.74 


12-53 
±0.76 


Vocabulary 
Ratio 


I5-7I 

±1.05 




16.58 
±1. 14 






IO.34 
±0.64 


IO.84 

±0.66 


Reading 
Ratio 


12.63 
±0.84 




12. 14 
±0.84 






11.82 
±0.73 


n.36 
±0.69 


Completion 
Ratio 


12.34 

±0.82 




12.63 
±0.87 






10.85 
±0.67 


9.90 
±0.60 




Correlations of Ratios 










Nov 


, 1018 J 


une 


, IQIO NOV., IQIQ 


June, 1920 


Arithmetic and Vocabulary 










.60 
±.06 


•30 

±.08 


Arithmetic and Reading 










.70 
±.04 


•64 
±•05 


Arithmetic and Completion 








' ' 


.48 
±.0 7 


.61 

±•05 


Vocabulary and Reading 


± 


•34 

.08 


± 


.32 
09 


•57 
±.06 


•47 
±.0 7 


Vocabulary and Completion 


± 


•45 
.07 


± 


.36 
O8 


•53 
±.06 


•54 
±.06 


Reading and 


Completion 


± 


.61 

.06 


± 


.65 
.06 


.67 

±.05 


.67 

±•05 



Statistical Treatment of the Experiment 37 

the S. D. AccR 1920 is 9.09; the S. D. IQ is 19.24. It is obvious that 
the average amount of product per intelligence has increased, 
that the range of Ace R's has decreased (which means that factors 
causing disparities, other than intelligence, have been removed), 
and that the S. D. of the Ace R's is about one half the S. D. of the 
I Q's. M's are about equal so it is not necessary to use coefficients 
of variability. The variability of children, intelligence aside, is 
only one half what the variability is otherwise. The correlations 
when I Q =X, Ace Ri9i8= Y and Ace Ri92o = S and when Ace R = 
average of Vocabulary, Reading and Completion Ratios, are: 1 

rx.Y. = — 602 

*x.s. = -493 
r Y .s. = +.549 

The remaining disparity is then due to something which is in 
negative correlation with intelligence. 
The number of cases here is only 48. 
The P. E.'s are then as follows: 

P. E. M P. E. SD . 

X 1. 91 1.35 

Y 1. 1 1 0.79 

5 o . 90 o . 64 

P. E.r x .Y. = 06 

P. E.r x .s. = .08 

P. E.r Y .s. = .07 

The differences between the M's and between the S. D.'s of our 
1918 and our 1920 Ace Q's; namely, 102.78 — 98.24=4.54 and 
11.17 — 9.09 = 2.08, have formed a step in the argument. We must 
have the P. E.'s of these amounts in order to establish the reliabil- 
ity of the quantitative indices we employ: 



P. E. diff = V p. E. x + P. E. Y - 2 r XY P. E. x P. E, 



P - E m. 20 - m. 18 = 0.94 

p - e -s.d.. 1s - S.D.. 2n = °47 



1 No arithmetic was given in 191 8, therefore arithmetic was not used in these 
averages. 



38 The Accomplishment Ratio 

These differences are then reliable. If the same data were 
accumulated again in the same way with only 48 cases, the chances 
are even that the 4.54 would be between 3.50 and 5.48 and the 2.08 
between 1.61 and 2.55. That there would be positive differences 
is practically certain, since the difference between the means is 
over four times as large as its P. E., and the difference between 
the S. D.'s over four times as large as its P. E. 

To make still more certain this observation of positive amount 
in M of second testing minus M of first testing and in S. D. of 
first testing minus S. D. of second testing (AccR), which means 
an increase in central tendency of Ace R's and a decrease in spread 
of Ace R's under special treatment, we have listed in Table 13 
the means and standard deviations of Subject Ratios of each 
test for each period and the intercorrelations of these Subject 
Ratios. These do not include exactly the same children in each 
period but are inclusive of all grades for all periods. They are a 
measurement of increased efficiency of the school as a whole, 
rather than of any one group of children; though, of course, the 
bulk of the children have representation in each of these indices. 
Too much continuity is not to be expected from June, 1919, to 
November, 1919, as the children are different. Comparison should 
always be from November to June. 

These tables bear out the fact presented by Ace R. It is clear 
that there is a marked development in the S. R.'s, both by increase 
of M. and decrease of S. D. The decrease of correlation between 
S. R.'s is not so marked, but neither is the negative correlation 
between Ace R and I Q much less in June, 1920, than in November, 
191 8. The association of achievements in terms of intelligence is 
very probably due to mistreatment, since it is in negative correla- 
tion with I Q, as a general inherited ethical factor could not be. 

We will note that the Arithmetic Ratios are in as high positive 
association with the Reading Ratios as the Vocabulary Ratios are 
with the Reading Ratios. This makes it highly improbable that 
the intercorrelation of these remnants is due, to any large extent, 
to common elements in the test or to specific abilities. The com- 
mon interassociation of all Ratios seems to point to the operation 
of some common factor other than intelligence as a determinant 
of disparity in school progress. It would be easy to identify this 
as the part of Burt's "General Educational Factor" which is not 
intelligence — that is, industry, general perseverance and initia- 



Statistical Treatment of the Experiment 39 

tive — were it not for the fact that this same influence stands in 
negative association to intelligence. It is our belief that it is the 
influence of a maladjusted system of curricula and methods which 
accounts for these rather high interassociations of achievements, 
irrespective of intelligence. 

SUMMARY 

The association of abilities in arithmetic, reading, and com- 
pletion with intelligence is markedly raised by special treatment. 
Disparities of educational product are therefore to a great extent 
due to intelligence. (Tables 2, 3, 5, 7, 8, 9, 10 and II.) 

The remnants (intelligence being rendered constant by division 
of each S Q by I Q) intercorrelate about .5. If there were special- 
ized inherited abilities, these intercorrelations would not all be 
positive nor would they be as uniform. (Tables 6 and 13.) 

The averages of these remnants, for reading, vocabulary, and 
completion, correlate —.61 in 1918 and —.49 in 1920 with I Q. 
These remnants are in negative association to intelligence. If 
the intercorrelations of these remnants were due to a ' 'General 
Factor," this correlation would not be negative. 

Therefore intelligence is far and away the most important 
determinant of individual differences in product. 

As part of the relation between tests, irrespective of intelligence, 
is due to common elements in the tests, this reasoning becomes 
still more probable. 

General factor in education, as distinct from intelligence, has 
not been separated here from inherited bases of ambition, con- 
centration, and industry. It seems out of our province to conjure 
up some inherited complex of abilities other than intelligence, 
specialized inherited abilities, or proclivities and interests tending 
to thorough prosecution of school work. I have therefore meant 
this last by the general factor. 

McCall has correlations varying continually in size from — .63 
to +.98 between various measurements of a group of 6B children. 1 
The abilities involved were not pushed as are those considered here. 
Some of the low correlations are no doubt indications of low asso- 
ciation because of the way children are, not the way they might be 

1 William Anderson McCall: Correlations of Some Psychological and Educational 
Measurements, Teachers College Contributions to Education, No. 79. 



40 The A ccomplishment Ratio 

by heritage; still others, such as handwriting and cancellation 
(unless bright children do badly in cancellation tests because they 
are more bored than the others), are correlated low or negatively 
with intelligence when the correlation is at its maximum. Such 
results as those of McCall serve as a guide not to argue about 
other tests by analogy. It is necessary to find which traits and 
abilities can be pushed to unity in their relation to intelligence and 
which, like handwriting, are practically unrelated to general men- 
tal power. 

It is well to know about music tests and such tests as Sten- 
quist's mechanical ability test when the correlation with intelligence 
is pushed, before we decide whether the quality measured is a 
manifestation of specific talent or general intelligence. 

Cyril Burt obtained data much like that presented here except 
that instead of getting rid of the influence of intelligence and finding 
determinants for the remnants of disparity, he built up a hierarchy 
of coefficients as they would be if they were due entirely to a common 
factor and compared these with his obtained r's. I will present his 
conclusions with regard to a general factor which are in substantial 
though not complete agreement with those advanced here. 

"Evidence of a Single Common Factor. 

"The correlations thus established between the several school 
subjects may legitimately be attributed to the presence of common 
factors. Thus, the fact that the test of Arithmetic (Problems) 
correlates highly with the test of Arithmetic (Rules) is most natur- 
ally explained by assuniing that the same ability is common to 
both subjects; similarly, the correlation of Composition with Arith- 
metic (Problems) may be regarded as evidence of a common factor 
underlying this second pair; and so with each of the seventy-eight 
pairs. But is the common factor one and the same in each case? 
Or have we to recognise a multiplicity of common factors, each 
limited to small groups of school subjects? 

"To answer this question a simple criterion may be devised. It is 
a matter of simple arithmetic to reconstruct a table of seventy-eight 
coefficients so calculated that all the correlations are due to one 
factor and one only, common to all subjects, but shared by each in 
different degrees. Such a theoretical construction is given in 
Table XIX. In this table theoretical values have been calculated 
so as to give the best possible fit to the values actually obtained in 



Statistical Treatment of the Experiment 41 

the investigation, and printed in Table XVIII. It will be seen 
that the theoretical coefficients exhibit a very characteristic arrange- 
ment. The values diminish progressively from above downwards 
and from right to left. Such an arrangement is termed a 'hierarchy.' 
Its presence forms a rough and useful criterion of the presence of a 
single general factor. 

"On turning to the values originally obtained (Table XVIII.) it 
will be seen that they do, to some extent, conform to this criterion. 
In certain cases, however, the correlations are far too high — for 
instance, those between Arithmetic (Rules) and Arithmetic (Prob- 
lems), and again Drawing and both Handwork and Writing 
(Quality) . Now these instances are precisely those where we might 
anticipate special factors — general arithmetical ability, general 
manual dexterity — operating over and above the universal factor 
common to all subjects. These apparent exceptions, therefore, are 
not inconsistent with the general rule. Since, then, the chief 
deviations from the hierarchical arrangement occur precisely where, 
on other grounds, we should expect them to occur, we may accord- 
ingly conclude that performances in all the subjects tested appear 
to be determined in varying degrees by a single common factor. 

"Nature of the Common Factor. 

"What, then, is this common factor? The most obvious sugges- 
tions are that it is either (1) General Educational Ability or (2) 
General Intelligence. For both these qualities, marks have been 
allotted by teachers, quite independently of the results of the tests. 
The correlations of these marks with performances in the tests are 
given in the last two lines of Table XVIII. 

"Upon certain assumptions, the correlation of each test with the 
Hypothetical Common Factor can readily be deduced from the 
coefficients originally observed. These estimates are given in the 
last line but two of the table. They agree more closely with the 
observed correlations for General Educational Ability, especially 
if the latter are first corrected for unreliability. (Correlations: 
Hypothetical General Factor coefficients and General Educational 
Ability coefficients .86; after correction .84. Hypothetical General 
Factor coefficients and General Intelligence coefficients .84; after 
correction .77.) We may, therefore, identify this hypothetical 
general factor with General Educational Ability, and conclude 



42 The A ccomplishment Ratio 

provisionally that this capacity more or less determines prowess in 
all school subjects. 

"The high agreement of the estimated coefficients with the intelli- 
gence correlations suggest that General Intelligence is an important, 
though not the only factor in General Educational Ability. Other 
important factors are probably long-distance memory, interest and 
industry. It is doubtless not a pure intellectual capacity; and, 
though single, is not simple, but complex." 

1 Cyril Burt: The Distribution and Relations of Educational Abilities, pp. 53-56. 



PART III 

THE PSYCHOLOGICAL CONCLUSIONS OF 
THE EXPERIMENT 

THE NEGLECT OF GENIUS 

Schools of to-day are organized and administered so as to yield 
less chance to a child to obtain as much information as is possible 
for him to have in direct proportion to his mental ability. The 
correlation between accomplishment and intelligence (using Ace R, 
the average of Reading, Vocabulary, and Completion Ratios with 
I Q) was — .61 in November, 1918, and — .49 in June, 1920, in the 
Garden City public school. The regrading and special promotion 
work from November, 1918, to June, 1920, reduced the handicap 
of brightness, but could not obliterate the sparsity of returns per 
increment of capacity in the upper reaches of the intelligence. 
Further, work along this same line done by A. J. Hamilton in the 
Washington School, Berkeley, California, indicates that this was 
not a peculiarity of the school at Garden City. 

The wide range of abilities which we know exists in pupils of any 
one age makes it impossible to adjust our formal education to the 
extremes. Much adjustment has been made in favor of the lower 
extreme, but little has been done for our genius. Of course the work 
with extreme subnormals is conceived and prosecuted more in the 
sense of clearing them away for the good of those remaining than 
of fitting education to their own needs. We are neglecting, however, 
our duty to those whom nature has endowed with the essentials of 
leadership. They do not interfere quite as much with ordinary 
classroom procedure, but they are greater social assets and need 
special treatment to develop them rather than to let others develop 
better. 

Neither of the extreme groups is certain of getting the normal 
stamina necessary for good citizenship. Neither group forms good 
habits of study nor accumulates such information as it might. 
Being aware of this discrepancy between the gift and the recipient, 
we have made our lessons easier and we have segregated the lower 
percentile. There is much more to be done. We must adapt 



44 The Accomplishment Ratio 

education to at least five varying classes in order to reduce the 
spread within each to a commodious span. But the genius is the 
most important and should have the greatest claim to our immediate 
attention. 

First, our social needs demand special attention for the genius 
in order that we may better exploit our best nervous resources. 
Second, our educational needs demand it since the very bright as 
well as the very stupid disrupt calm and cogent classroom procedure. 
Third, they themselves demand it in order that they may, even 
when they do function as leaders, be happier in that function, since 
now they often lose much in social contact by peculiarities which 
prevent an integration of their "drives" into a harmonious economy 
of tendency. These peculiarities come from their continuous mal- 
adjustment, since when they are with children of their own mental 
maturity they are physically and physiologically handicapped; 
when they are with children of their own size and muscular equip- 
ment they are so far mentally superior that they are unhappily 
adjusted. Only classification on a large scale will allow sufficient 
numbers of them to congregate to correct this. 

I am reminded of a boy ten years old whose I Q on the Terman 
test was 172. He defined a nerve as the "conduction center of 
sensation" and, when asked to explain, did so in terms of sensation 
of heat and motive to withdraw. He explained the difference 
between misery and poverty thus: "Misery is a lack of the things 
we want; poverty is a lack of the things we need." How can we 
expect a boy like this to grow into a normal citizen if we do not 
provide the companionship of peers in mentality and in physique? 

Fourth, our eugenic needs demand it, since we are not conserving 
this, our chiefest asset, genius. Unless we conserve better these 
rare products, the standard deviation of the intelligence of humanity 
will keep shrinking as we select against imbeciles and against genius 
as well. The waste of a genius who becomes an intellectual dilet- 
tante, as many now in fact do, is double. We lose what he might 
do for society; he does not marry and we lose the potentiality of 
his highly endowed germ-plasm. 

And they do become dilettantes when special treatment is not 
given . I know of a young man who was first of his high-school class , 
who got all A's his first year in College (at Wisconsin), and all 
A's his second year (at Harvard); and then he began to read all 
manner of literature with no schema of expression, no vocation, 



The Psychological Conclusions of the Experiments 45 

because, as he said, all college courses are so stupidly easy. He 
attended no lectures and read none of the books in one course, and 
then two days before the examination he was taunted with not 
being able to pass this course. He spent two nights and two days 
studying, and he received B in the course. But now he is a failure 
because he has no organized, purposive schema of expression; 
he was always in classes with people less fortunately endowed than 
he, and so he never had a chance. 

On these four counts then we must segregate our genius: (1) 
Social exploitation of our resources. (2) Educational procedure for 
the sake of other children as well as for them. (3) Happiness for 
them, organization of their trends, and formation of social habits. 
(4) Biologic conservation of great positive deviation from average 
human intelligence. 

IS GENIUS SPECIALIZED? 

This genius is of various kinds, political and business leaders, 
scientists and artists. Have they then the same inherited nervous 
structure with regard to abilities and capacities as distinct from 
interests? We know that they must have something in common, 
something that we call intelligence, power of adaptation. Calling 
this the nervous chemistry, the way the nervous system acts its 
quality, we must still know whether we have also an inherited 
nervous physics to deal with, or a further inherited nervous chem- 
istry which predisposes to specific ability. Are there inherited 
capacities or predispositions to ability? We are in a position to 
answer this question with regard to the elementary school subjects, 
and are tempted here into a more general discussion of the matter 
in hand. 

The need to clarify our view on what is inherited and what is due 
to environment can be clearly envisaged in terms of our teachers. 
Whatever psychologists may mean by "predisposition to ability" 
it is quite certain that teachers make no distinction between this 
and the inheritance of a capacity. They feel that some children 
figure better than they read, and others read better than they 
figure, "by nature," and there their obligation ends. If it is a 
grave matter that we shoulder the burden of bringing a child to his 
optimum achievement, then it is an immediate duty that we find 
how much of the failure to produce product of one kind or another 
is due to unremovable factors, and how much is due to our in- 



46 The Accomplishment Ratio 

adequacy. So, too, we have much loose discussion about finding 
out what children can do and want to do in the way of vocational 
diagnosis, — loose because it assumes that children are born with 
definite vocational capacities. Certainly we can do much more in 
the way of development and much more in the way of preparation 
for social needs if we know just how much "predisposition to ability" 
means. The teacher interprets it to mean about what was meant 
by the turtle that held up Atlas who held up the world. She makes 
no real distinction between predisposition to ability and specific 
ability, just as there was no real causal distinction between the 
turtle and Atlas. She then gets at her conception of intelligence 
additively, — a summation of school abilities. 

The correlation of teachers' judgment of "power of adaptation," 
carefully explained, and marks given six months previously by the 
same teachers was .82. The correlation of this same average 
judgment with the average of thirteen intelligence tests was only .58. 
These teachers obviously reached their conclusions of the intelligence 
of a child in the same way as they reached their conclusions of 
what marks he earned in their subjects. 

The unit characteristics which make up what we describe in 
terms of gross behavior as intelligence must of course be many. 
No one denies that if we knew just what these units were we could 
describe two possible manifestations of what we now call intelligence, 
of which one person could do one only and another person could 
do the other only because of the particular combinations of the 
units inherited. This would constitute inheritance of predisposition 
to special capacities. But it is not the same to assume that the 
vocations and aptitudes desirable in a world such as ours have 
specialized inherited bases. It is far more probable that substan- 
tially the same inherited characteristics are necessary to success in 
all the gross cross-sections of behavior which we call vocations and 
abilities. 

As the unit characteristics are certainly not so closely allied to 
our social needs as "mechanical intelligence" and "social intelli- 
gence" or even "rote memory for numbers," we may not even 
distinguish presence of any five hundred elements from presence of 
any other five hundred elements in terms of what we now measure 
as intelligence. It is just as likely that all the elements of intelligence 
are necessary for every vocation and that all contribute to success 
of any one kind as it is likely that some are necessary for one voca- 
tion and others for another. 



The Psychological Conclusions of the Experiments 47 

This is a question of more or less. I believe that the amount to 
which a person's specific talents, his vocation as distinct from his 
general power, are shaped by the combinations of elements which 
make up his inheritance, is much less than believed by Francis 
Gal ton, who says: "There cannot then remain a doubt but that 
the peculiar type of ability that is necessary to a judge is often 
transmitted by descent." And again: "In other words, the com- 
bination of high intellectual gifts, tact in dealing with men, power 
of expression in debate, and ability to endure exceedingly hard work, 
is hereditary." 1 

I believe that the amount of influence which inheritance has upon 
the kind of thing a man does in life has been overestimated; that 
the inherited factors influence more the way in which he shall do 
whatever the environment influences him to do. This leaves plenty 
of play for the close correlation between parents and children in 
both intelligence and vocation. The former is the result of inherit- 
ance, the latter is the result of environment. All competent 
psychologists would agree to-day to less specific inheritance than a 
basis, for instance, for the distinction in vocation of minister and 
orator; and more specific inheritance than for such a statement 
as "We inherit how well we will do, we learn what we will do." 
There would be substantial agreement to the statement that the 
inherited nervous bases of a very intelligent plumber are more like 
those of a very intelligent statesman than like those of a stupid 
plumber. This question is, how much inheritance we can conceive 
of as being made up of neuro-chemical elements determining us to 
do one kind of a thing rather than another. 

Interpretation statistically of one thousand possible elements, 
simply viewed as present or absent, and again simply viewed only 
as combinations and not permutations, would mean that the less 
the intelligence the more specific the inheritance. The most intel- 
ligent man alive could, by what he is born with, do anything since 
he has all of the one thousand factors, all of which help him in the 
prosecution of any venture. But the fewer elements he has the 
less well he does most things, and when lacking certain elements 
he has lost the capacity to do some things more completely than 
others. (I have neglected physiological characteristics necessary to 
an ability. A deaf man certainly is handicapped in music. I speak 

1 Quotations from Galton: Hereditary Genius, '92, pp. 61-62 and pp. 103-104. 



48 The A ccomplishment Ratio 

of possible mental capacities.) Such a view leaves scope for some 
degree of special abilities. It accounts for the idiot-savants, it 
accounts for the cases where genius is diverse as well as where it is 
not though it would demand that specialized genius be very rare 
and that inherited specialization be much rarer in the upper than 
in the lower reaches of intelligence. It allows for such cases as 
Galileo, whose father was a composer, as well as the cases cited by 
Gal ton. Heredity need not imply the same kind of genius though 
it does suggest it, whereas the environment backs up this inherited 
implication. We further can here absolutely resent an inheritance 
of such things as ability in the common school subjects without 
being involved in a view to deny the inheritance of a predisposition 
to mechanical rather than musical successes. 

Observation of brilliant children would corroborate this view. 
They can do anything. Observation of the mentally deficient is 
equally encouraging to this view. It has always been puzzling that 
they seem to do a few things much better than others. According 
to this conception there would be a negative correlation between 
intelligence and specialized inheritance. 

We will then consider each inherited element, not as music or as 
science, but rather as an element of intelligence which will help in 
all lines of work, but which may be a little more necessary for 
some than others. This is a predisposition in a true sense. If a 
man had only one element out of one thousand, he could do only 
a few things. If he had all thousand he could do everything. 
Inheritance of ability is not in terms of units valuable to us socially, 
but only in terms of undefined nervous elements; and we may con- 
ceive of specialization, and still hold that there be less, the more 
intelligent a man is. 

To make the matter still more concrete, imagine two men each 
of whom have 900 of the hypothetical 1000 elements, this being a 
value of +3 S. D. from the mean intelligence of the human race. 
One is a composer, the other financier. According to this view the 
greatest number of their inherited bases on which they could 
differ would be 100 of the 900 elements. The other 800 must be 
alike. Assuming that all of the elements contribute to all of the 
activities, but that some of them are more essential to some activi- 
ties than to others, we could in this case say that the 100 which are 
different decided in some measure the vocation of each man. But 
it is much more probable that they overlap in 850 and that each 



The Psychological Conclusions of the Experiments 49 

has only 50 distinct elements, and further that the 50 which are 
distinct in each would not all be such as to influence one kind of 
ability rather than another. Then these two men, had they inter- 
changed environments, would probably have interchanged vocations 
in that transaction. For the purposes of this discussion we treat 
physiological inherited features (such as hearing), as environment, 
as we are considering the mental capacity of composer as distinct 
from the necessary conditions to its development. According to 
this view, then, we account easily for the versatility of genius, which 
is so apparent in such accounts as Terman's The Intelligence of 
School Children. 1 Also, though very infrequent, we account for 
the genius who could not have done other things as well as those he 
did. 

Let us consider the case of negative deviates, say 3 S. D. from 
the mean intelligence of the human race. Two men each have 100 
of the 1000 hypothetical elements. It is much more probable here 
than not, that an appreciable amount of the 100 elements would 
be distinct in each person, though it is improbable that they would 
often be such as to form the basis of an "ability." This then would 
account for specific abilities amongst morons and also for the 
presence but rarety of idiot-savants. Also since there are a limited 
number of such combinations possible and since many overlap for 
all practical purposes, we would account for the common likenesses 
as well as the relatively more uncommon extreme differences. This 
view is consistent with an examination of the data of this thesis 
which are contrary to the common belief in special abilities or to 
a view of inheritance of units which are actually the goals of 
education and the uses of a civilization too recent to leave its 
imprint on inheritance. We found no unremovable predispositions 
to one school subject more than to the others in any of the children. 
We would thus argue that such predispositions as to mathematics 
or to oratory are extremely rare and cannot be used as rules by 
which to interpret human nature. 

Woodworth says in a criticism of McDougall's view of instincts: 
"What he here overlooks is the fact of native capacities or rather, 
the fact that each native capacity is at the same time a drive towards 
the sort of activity in question. The native capacity for mathe- 

1 Terman, Lewis: The Intelligence of School Children. Boston: Houghton Mifflin, 
1919. 



50 The Accomplishment Ratio 

ma tics is, at the same time, an interest in things mathematical and 
in dealing with such things. This is clearly true in individuals 
gifted with a great capacity for mathematics." 1 

I do not wish to become involved here in a discussion of the 
original nature of man on the instinctive side. I wish merely to 
rebel at the assumption of specific inheritance of abilities that are 
really sociological units. Mathematics is an ability which is useful 
to us, which we have come to encourage in education. But it is a 
man-made unit. There is no reason to believe that the inherited 
components of mentality are in any direct way related to such 
talents as mathematics or music. The units may vaguely predis- 
pose, but the units are not mathematics and music. We may say 
that the inherited physical and chemical units of the nervous 
system may be so distributed as to predispose one man to mathe- 
matics, and another to music, but we must not argue for inherited 
interests as correlates. The evidence is all that the inherited 
nervous chemistry of the individual is what on the side of behavior, 
we define as intelligence — power of adaptation. We may logically 
fall back on the inheritance of predisposition to ability, meaning 
thereby the inheritance of such nervous qualities as will better 
fit the individual to cope with mathematical than with musical 
situations; but if we adopt this cautious ground in disputation we 
cannot argue in another matter for an inherited interest in mathe- 
matics, innate because of the inborn mathematical talent. If the 
inherited qualities merely predispose they merely delimit; just as 
a man born without arms would probably not become a great base- 
ball player, nor a deaf man a great musician, nor a man with poor 
motor control a skilled mechanic — so we are predisposed nervously 
for capacities. Hence can we argue that the inborn root of the 
interest is the capacity? Is it not safer to assume that interests in 
success, approval of fellowmen and general mental activity led to 
the development of the capacity by virtue of a favorable environ- 
ment, and led by the same environment to interests centered about 
its activity? 

It is far from my intention to say that inheritance is not as 
specific nervously as it is in matters of blood pressure and texture 
of skin. As we, in our limited knowledge, still define abilities in 
terms of behaviour and not by nervous elements, my contention i 

1 Woodworth, R. S.: Dynamic Psychology, p. 200. New York: Columbia University 
Press, 1918. 



The Psychological Conclusions of the Experiments 51 

that intelligence should be regarded as the sum total of this in- 
heritance, much as general strength is, in terms of the body. We 
have still to find the component units of this intelligence. We can 
then define predisposition to ability. To split intelligence into 
inherited units of mathematics, reading, composition, mechanics, 
etc., is as unjustifiable as to split inherited vigor of body into base- 
ball capacity, running capacity, climbing capacity, etc. Mathema- 
tics and music are what we do with intelligence, not what intelli- 
gence is made of. Of course everyone agrees to this. The lack of 
emphasis upon the chance that the inherited units are general in 
their application, that the same inherited elements are involved in 
many of the behavior complexes which we call traits and abilities, 
is what confuses the situation. 



CURRENT PSYCHOLOGICAL OPINION 

We must know what these elements are, and how many contribute 
to which capacities. Then we can decide the question of specialized 
inheritance. In all crude behavior data it is impossible to separate 
the influence of nature and nurture. A theory of specialized in- 
heritance will inevitably infringe upon common sense in its claims. 
Of the following statements, it would be easier for most of us to 
endorse 1 and 2 than 3 and 4, whereas few would agree with 5 
and 6. 

1. "Unless one is a blind devotee to the irrepressibility and 
unmodifiability of original nature, one cannot be contented with 
the hypothesis that a boy's conscientiousness or self-consciousness 
is absolutely uninfluenced by the family training given to him. Of 
intelligence in the sense of ability to get knowledge rather than 
amount of knowledge got, this might be maintained. But to prove 
that conscientiousness is irrespective of training is to prove too 
much." (Thorndike, Educational Psychology, III, pp. 242.) 

2. "Some attempts have been made to apply these laws to 
behavior complexes, but as yet psychology has provided little 
foundation for such studies. The most thorough-going attempts 
have been made with human mental traits and some evidence has 
been collected here in favor of the view that differences in the 
instinctive behavior of individuals are inherited according to Men- 
delian ratios. But in the field of human psychology too little is known 
of the genesis of character, of the distinction between nature and 



52 The Accomplishment Ratio 

acquired behaviour to provide a very firm foundation for the work of 
the geneticist.'" (Watson, Behaviour, p. 156. Italics are mine.) 

3. "Even, however, when we omit the trades as well as the cases 
in which the fathers were artists, we find a very notable predomin- 
ance of craftsmen in the parentage of painters, to such an extent 
indeed that while craftsmen only constitute 9.2 per cent among 
the fathers of our eminent persons generally, they constitute nearly 
35 per cent among the fathers of the painters and sculptors. It is 
difficult to avoid the conclusion that there is a real connection 
between the father's aptitude for craftsmanship and the son's 
aptitude for art. 

"To suppose that environment adequately accounts for this 
relationship is an inadmissible theory. The association between 
the craft of builder, carpenter, tanner, jeweller, watchmaker, wood- 
carver, rope-maker, etc., and the painter's art is small at the best 
and in the most cases non-existent." (Ellis, quoted in Thorndike, 
Educational Psychology, III, p. 257.) 

4. " — the statesman's type of ability is largely transmitted or 
inherited. It would be tedious to count the instances in favor. 
Those to the contrary are Disraeli, Sir P. Francis (who was hardly 
a statesman, but rather bitter a controversialist) and Horner. 
In all the other 35 'or 36 cases in my Appendix, one or more states- 
men will be found among their eminent relations. In other words, 
the combination of high intellectual gifts, tact in dealing with men, 
power of expression in debate and ability to endure exceedingly 
hard work, is hereditary." (Gal ton, Hereditary Genius, pp. 103, 
104.) 

Thorndike comments on this last quotation: "Of course there 
is, in the case of all of Gal ton's facts the possibility that home sur- 
roundings decided the special direction which genius took, that 
really original nature is organized only along broad lines. More- 
over, it is difficult to see just what in the nervous system could 
correspond to a specialized original capacity, say, to be a judge. 
Still the latter matter is a question of fact, and of the former issue 
Galton's studies make him the best judge. We should note also 
that it is precisely in the traits the least amenable to environmental 
influence such as musical ability, that the specialization of family 
resemblance is most marked." 

This cautious and sagacious commentary is in marked contrast 
to the following: 



The Psychological Conclusions of the Experiments 53 

5. "But no training and no external influence can entirely super- 
sede the inborn tendencies. They are the product of inheritance. 
Not only unusual talents like musical or mathematical or linguistic 
powers can be traced through family histories, but the subtlest 
shades of temperament, character and intelligence can often be 
recognized as an ancestral gift." (Munsterberg: Psychology, 
General and Applied, p. 230.) 

6. "Statistical studies which covered many characteristic 
opposites like industrious and lazy, emotional and cool, resolute 
and undecided, gay and depressed, fickle and constant, cautious 
and reckless, brilliant and stupid, independent and imitative, 
loquacious and silent, greedy and lavish, egoistic and altruistic 
and so on, have indicated clearly the influence of inheritance on 
every such mental trait." (Munsterberg, Psychology, General and 
Applied, p. 237.) 

Undoubtedly Munsterberg here refers to the data accumulated 
by Heymans and Wiersma since they used such opposites as these, 
and also used what might be called statistical methods. Speaking 
of the same data Thorndike says: 

"In view of the insecurity of their original data it seems best 
not to enter upon an explanation of their somewhat awkward 
method of measuring the force of heredity, and not to repeat 
the figures which are got by this method. Also they do not attempt 
to estimate an allowance for the influence of similarity in home 
training, though they state that some such allowance must be 
made." {Educational Psychology, III, p. 262.) 

Hollingworth and Poffenberger, commenting on the data of 
Gal ton and Ellis mentioned in the quotation above, say: 

"Francis Gal ton has made a statistical study of the inheritance 
of specified mental abilities and found that the abilities required 
for success as a judge, statesman, minister, commander, poet, 
artist, and scientific man, are inherited. But the nature of his 
data makes him unable to make exact allowances for influences 
of training and environmental influences. Consequently, his 
figures might really show general intelligence to be inherited and 
the form of its expression to be dependent upon environment. 

"Other investigators, among them F. A. Woods and Havelock 
Ellis, have made similar statistical studies and conclude that 
there is inheritance of even such qualities as temper, common 
sense, and the like, but these reports are also subject to the same 



54 The A ccomplishment Ratio 

complicating influence of environment." {Applied Psychology, 

P- 43-) 

It can readily be seen, from these quotations, that there is funda- 
mental disagreement among psychologists with regard to the 
inheritance of specific ability, — fundamental disagreement in 
three ways: (1) Interpretation of Gal ton's and Ellis's data. (2) 
Opinion on the matter. (3) Degree of precision possible in giving 
judgment. 

We have noted that it is very difficult to understand what the 
neural bases for such special abilities as Galton speaks of could 
be; that they are social, not neural or psychological units. A 
view of a large number of inherited elements all of which contribute 
to what we call general intelligence and each of which is slightly 
more necessary to some vocation than others, would account for 
all the observed facts, is neurally imaginable, and does not need 
to view ability to be a " judge" or "artistic talents" as biological 
entities. It further explains the differences in their limited abilities 
of mentally deficient children. 

Burt says in this connection: "Among children of special (M.D.) 
schools, the evidence for a general factor underlying educational 
abilities and disabilities of every kind is not so clear. In ad- 
ministrative practice, "mental deficiency" implies among different 
children deficiencies in very different capacities, both general and 
specific." (Cyril Burt: The Distribution and Relation of Educa- 
tional Abilities , p. 83.) 

For these reasons it is justifiable to attempt to present evidence 
of the inheritance of school abilities with a view to showing that 
school abilities are not dependent upon special inherited aptitudes, 
as teachers so often assume, but that general intelligence is the 
only inherited cause of disparity in product. Investigations where 
the correlation between educational product and intelligence, 
irrespective of chronological age, was less than around .75, used 
data where many removable causes were not removed, and con- 
sequently measured results of the environment as well as heredity. 
A case such as this follows: 

"The influence of inheritance upon a very specific mental quality, 
namely, spelling ability, has been tested experimentally, although 
here there is some difficulty in separating the influence of heredity 
from that of environment. Earle studied the spelling ability of 
180 pairs of brothers and sisters who had uniform school training 



The Psychological Conclusions of the Experiments 55 

and found a correlation of .50. This means that if one child devi- 
ated by a certain amount from the average child in spelling ability, 
his brother or sister would deviate from the average child just 
half as much; that is, he would resemble his brother or sister to 
that extent." (Hollingworth and Poffenberger: Applied Psy- 
chology, p. 44.) 

The data presented in this thesis indicate that that correlation 
could have been pushed as high as the r between the intelligence 
of the pairs of brothers. In other words, a child could be made 
to resemble his brother as nearly in spelling ability as he did in 
intelligence. All disparity could be reduced to that of general 
intelligence. Then intelligence alone is inherited as far as the 
data here presented have any bearing on the matter in hand. 
The influence of environment is in this case a matter of no conse- 
quence, since the subjects all had the same schooling, and home 
influence does not as a rule teach children to spell; but the data 
are not irrespective of the influence of intelligence. 

INDICATIONS OF THE GARDEN CITY DATA 

Table 3 presents intercorrelations between I Q and quotients in 
the various subjects. The correlations are in each instance ir- 
respective of chronological age since all quantitative indices are 
expressed as quotients. We have seen that they go up from Sep- 
tember, 191 8, to June, 1920. Every possible means was used to 
push these correlations to their limit, to remove all removable 
factors. We have seen that the data show here, as in Tables 7 and 
8, that there is little association between traits which is not a result 
of differences in intelligence. Table 3 shows the same 48 children 
throughout. The r's are not corrected for attenuation. Though 
the r's are high throughout and go higher under special treatment, 
the association can still be more accurately registered by some 
attention to relation of the means and the S. D.'s. Two traits 
to be identical must have r = i.oo S. D.* = S. D >2/ and M % ^M y . 
We have seen that the r increases, M — M decreases and S. D. — 
S. D. regardless of sign decreases. (Tables 9, 10 and 11.) 

But as the S. D.'s of the Subject Quotients (though they do 
approach S. D. of I Q) sometimes go below the S. D. of I Q, we 
must know why. It is because the low I Q's do better per their 
intelligence than the high I Q's. We have seen above that the 
correlation between I Q and average of the Vocabulary, Reading, 



56 The Accomplishment Ratio 

and Completion Subject Ratios is —.61 in November, 1918, and 
— .49 in June, 1920. 

Then the ratio of achievement to intelligence is in definite 
relation to intelligence — a negative relation. It is this same 
tendency to adapt our education to a low level which has pre- 
vented a perfectiassociation between intelligence and the various sub- 
jects. The relation of one subject to another, irrespective of intelli- 
gence, would be zero if there were no other factors except intelligence 
responsible for the product. After two years of such attempts as 
an ordinary public school will allow, we have removed many of the 
causes of disparity and increased the association between potential 
progress and progress in arithmetic, reading and language. The 

correlations, correspondence of S. D.'s, and — ^— ^ — registered 

n 

in Tables 9,10, and 1 1 give evidence of this as does also the increase 
in the Ace R, an average of the Arithmetic, Reading, Vocabulary 
and Completion Ratios. (Table 13.) 

Are the unremoved causes other than intelligence unremovable? 
These causes might be, besides the unreliability of tests and the 
common elements in the tests, the specialized inheritance we have 
considered, ethical qualities of endurance, ambition, initiative and 
industry or a general factor. The correlations between Arith- 
metic Ratios and Reading Ratios and the other intercorrelations 
of Subject Ratios will yield us an index of how much of this remain- 
ing disparity is due to specialized inheritance. These intercor- 
relations for all years are embodied in Table 13. The partial 
correlations of quotients when intelligence is rendered constant 
will be found in Table 6. These intercorrelations, and the partials 
as well, give an indication of some general factor other than in- 
telligence since the r's irrespective of intelligence are uniform and 
all are positive. Only the correlation of arithmetic with vocabu- 
lary, intelligence being rendered constant, goes to zero. Though 
this might be due in part to common elements in the tests, it is 
more likely that there is another factor in operation. Inheritance 
of specific abilities could not have this uniform effect on the cor- 
relations. 

These correlations all being positive and the r's being very 
uniform, both correlation of ratios and the partials, makes the 
interpretation of specialized inheritance of ability extremely 
unlikely. The correlation of Arithmetic Ratios with Reading 



The Psychological Conclusions of the Experiments 57 

Ratios is higher in 1920 than that of Vocabulary Ratios with 
Reading Ratios. It leaves the possibility that the unremoved 
factors are inherited ethical differences or that they are a "general 
educational factor." The negative correlation of Ace R with 
intelligence, however, being as high as these positive remnants of 
interrelation, would tend to make more probable an interpretation 
of this as a remnant of disparity, intelligence accounted for, which 
is entirely due to the organization of our schools. 

All disparity not due to intelligence was worked on as far as it 
was possible. Thereupon the association of intelligence and edu- 
cational product increased markedly and the negative association 
of intelligence with achievement in terms of intelligence decreased 
somewhat. However, some association of abilities not due to 
intelligence remains. Exactly as much negative association of 
achievement in terms of intelligence, with intelligence, remains. 
So, when some of the disparities due to the environment have 
been removed and therefore the correlation of Arithmetic Ratio 
with Vocabulary Ratio and Reading Ratio has been decreased, 
the causes which contributed to a correlation such as lack of 
interest having been removed, there still remains some relation 
of school qualities. But there also still remains a negative associa- 
tion between this accomplishment and intelligence which means 
that we still have a remnant of such removable influence as is due 
to badly adjusted curricula. 

This enables us to interpret our partials. The partials are not 
nearer zero because although we have partialed out the effect 
of intelligence, we have not partialed out the factor which controls 
the negative relation to intelligence of these very partial resultants, 
since that is the effect of the methods and curricula. Though we 
did advance bright pupils and give them more chance, we have 
not given them a chance proportionate to the stupid children. 
And that is true since we often wanted to advance pupils and were 
not allowed to; whereas we were never allowed to demote pupils 
except in particular subject matter. The stupid children were 
always at the frontier of their intelligence at the educational cost 
of the others. 

It is this remnant which has usually been interpreted as "general 
factor" or as inherited factors basic to initiative, ambition, and 
industry. The fact of importance is that these remnants, these 
marks of children independent of their intelligence, are associated 



58 The Accomplishment Ratio 

negatively with intelligence to the same degree that they are 
associated positively to each other. Unless we wish to assume 
that the "general factor" or the inherited bases of initiative and 
industry are associated negatively with intelligence we must account 
for the remnant in some other way. It seems far more reasonable 
to attribute this remaining association to the educational handicaps 
of intelligence which we were unable to remove. 

The original tendencies of man, as distinct from his original 
equipment, have not been considered in this study. If the quanti- 
tative differences in endowment of this kind were added to the 
denominator of our accomplishment ratio formula, we would 
have a better measure and better results. We share in this investi- 
gation a general limitation of educational psychology — the requisite 
technique to measure individual differences of instincts and the 
the ethical traits of which they are the predisposition. Industry, 
ambition, and initiative are not inherited units. They are, how- 
ever, the rules of an economy of expression and as such are de- 
pendent upon individual differences in strength of instinct. 

CONCLUSIONS 

1 . I Q can be used as a limit of school achievement expressed 

as SQ. 

. S(IQ-SQ) , - 

a Progress in — — may be used as a measure ol 

n 

school efficiency. 

SO 
b y-y^ may be used as a measure of individual efficiency. 

2. Correlations between intelligence and achievement are very 
different before and after the abilities are pushed. 

a Many r's are reported where conclusions are drawn as 
though they had been pushed . These conclusions should 
be restated. 

b Intelligence and achievement are far more closely associ- 
ated than has been assumed to date. 

3. Disparity of school product can be reduced to individual 
differences in intelligence. 

a Little specific inheritance of school abilities. 



The Psychological Conclusions of the Experiments 59 

b Little unremovable difference in industry, conscientious- 
ness and concentration. 
c Intelligence is the only inherited general factor. 

4. Negative association between Ace R and I Q. 

a To-day's educational procedure involves a handicap to 

intelligence. 
b The genius has been neglected. 



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